diff --git a/src/backend/to_dot.jl b/src/backend/to_dot.jl
index b001ada3..69e64f2f 100644
--- a/src/backend/to_dot.jl
+++ b/src/backend/to_dot.jl
@@ -1,26 +1,26 @@
 function to_dotstatic(operator::Type, id::Int, factor, subgraphs::AbstractVector{<:AbstractGraph}, subgraph_factors::AbstractVector)
     error(
-        "Static representation for computational graph nodes with operator $(operator) not yet implemented! " 
+        "Static representation for computational graph nodes with operator $(operator) not yet implemented! "
     )
 end
 
-function to_dotstatic(::Type{ComputationalGraphs.Sum}, id::Int, factor::F,subgraphs::Vector{Graph{F,W}}, subgraph_factors::Vector{F}) where {F,W}
+function to_dotstatic(::Type{ComputationalGraphs.Sum}, id::Int, factor::F, subgraphs::Vector{Graph{F,W}}, subgraph_factors::Vector{F}) where {F,W}
     node_temp = ""
     arrow_temp = ""
     if factor != 1
         opr_fac = "factor$(id)[label=$(factor), style=filled, fillcolor=lavender]\n"
-        opr_name =  "g$(id)_t"
-        node_str  = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
-        arrow_temp*= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
+        opr_name = "g$(id)_t"
+        node_str = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
+        arrow_temp *= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
         node_temp *= opr_fac * node_str
     else
         opr_name = "g$id"
     end
     opr_node = opr_name * "[shape=box, label = \"Add\", style=filled, fillcolor=cyan,]\n"
     node_temp *= opr_node
-    for (gix,(g, gfactor)) in enumerate(zip(subgraphs, subgraph_factors))
-        if gfactor!= 1
-            factor_str = "factor$(g.id)_$(id)_$gix[label=$(gfactor), style=filled, fillcolor=lavender]\n" 
+    for (gix, (g, gfactor)) in enumerate(zip(subgraphs, subgraph_factors))
+        if gfactor != 1
+            factor_str = "factor$(g.id)_$(id)_$gix[label=$(gfactor), style=filled, fillcolor=lavender]\n"
             subg_str = "g$(g.id)_$(id)_$gix[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
             node_temp *= factor_str * subg_str
             arrow_temp *= "factor$(g.id)_$(id)_$gix->g$(g.id)_$(id)_$gix[arrowhead=vee,]\ng$(g.id)->g$(g.id)_$(id)_$gix[arrowhead=vee,]\n"
@@ -29,7 +29,7 @@ function to_dotstatic(::Type{ComputationalGraphs.Sum}, id::Int, factor::F,subgra
             arrow_temp *= "g$(g.id)->$opr_name[arrowhead=vee,]\n"
         end
     end
-    return node_temp,arrow_temp
+    return node_temp, arrow_temp
 end
 
 function to_dotstatic(::Type{ComputationalGraphs.Prod}, id::Int, factor::F, subgraphs::Vector{Graph{F,W}}, subgraph_factors::Vector{F}) where {F,W}
@@ -37,27 +37,27 @@ function to_dotstatic(::Type{ComputationalGraphs.Prod}, id::Int, factor::F, subg
     arrow_temp = ""
     if factor != 1
         opr_fac = "factor$(id)[label=$(factor), style=filled, fillcolor=lavender]\n"
-        opr_name =  "g$(id)_t"
-        node_str  = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
-        arrow_temp*= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
+        opr_name = "g$(id)_t"
+        node_str = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
+        arrow_temp *= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
         node_temp *= opr_fac * node_str
     else
         opr_name = "g$id"
     end
-    opr_node  = opr_name * "[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n" 
+    opr_node = opr_name * "[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
     node_temp *= opr_node
     if length(subgraphs) == 1
-        if subgraph_factors[1] ==1
+        if subgraph_factors[1] == 1
             arrow_temp *= "g$(subgraphs[1].id)->$opr_name[arrowhead=vee,]\n"
         else
-            factor_str = "factor$(subgraphs[1].id)_$(id)[label=$(subgraph_factors[1]), style=filled, fillcolor=lavender]\n" 
+            factor_str = "factor$(subgraphs[1].id)_$(id)[label=$(subgraph_factors[1]), style=filled, fillcolor=lavender]\n"
             node_temp *= factor_str
             arrow_temp *= "factor$(subgraphs[1].id)_$(id)->$opr_name[arrowhead=vee,]\ng$(subgraphs[1].id)->$opr_name[arrowhead=vee,]\n"
         end
     else
-        for (gix,(g, gfactor)) in enumerate(zip(subgraphs, subgraph_factors))
-            if gfactor!= 1
-               factor_str = "factor$(g.id)_$(id)_$gix[label=$(gfactor), style=filled, fillcolor=lavender]\n" 
+        for (gix, (g, gfactor)) in enumerate(zip(subgraphs, subgraph_factors))
+            if gfactor != 1
+                factor_str = "factor$(g.id)_$(id)_$gix[label=$(gfactor), style=filled, fillcolor=lavender]\n"
                 subg_str = "g$(g.id)_$(id)_$gix[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
                 node_temp *= factor_str * subg_str
                 arrow_temp *= "factor$(g.id)_$(id)_$gix->g$(g.id)_$(id)_$gix[arrowhead=vee,]\ng$(g.id)->g$(g.id)_$(id)_$gix[arrowhead=vee,]\n"
@@ -67,7 +67,7 @@ function to_dotstatic(::Type{ComputationalGraphs.Prod}, id::Int, factor::F, subg
             end
         end
     end
-    return node_temp,arrow_temp
+    return node_temp, arrow_temp
 end
 
 function to_dotstatic(::Type{ComputationalGraphs.Power{N}}, id::Int, factor::F, subgraphs::Vector{Graph{F,W}}, subgraph_factors::Vector{F}) where {N,F,W}
@@ -75,19 +75,19 @@ function to_dotstatic(::Type{ComputationalGraphs.Power{N}}, id::Int, factor::F,
     arrow_temp = ""
     if factor != 1
         opr_fac = "factor$(id)[label=$(factor), style=filled, fillcolor=lavender]\n"
-        opr_name =  "g$(id)_t"
-        node_str  = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
-        arrow_temp*= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
+        opr_name = "g$(id)_t"
+        node_str = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
+        arrow_temp *= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
         node_temp *= opr_fac * node_str
     else
         opr_name = "g$id"
     end
-    opr_node  = opr_name * "[shape=box, label = \"Pow\", style=filled, fillcolor=darkolivegreen,]\n" 
+    opr_node = opr_name * "[shape=box, label = \"Pow\", style=filled, fillcolor=darkolivegreen,]\n"
     order_node = "order$(id)[label=$N, style=filled, fillcolor=lavender]\n"
     node_temp *= opr_node * order_node
-    arrow_temp*= "order$(id)->$opr_name[arrowhead=vee,]\n"
+    arrow_temp *= "order$(id)->$opr_name[arrowhead=vee,]\n"
     if subgraph_factors[1] != 1
-        factor_str = "factor$(subgraphs[1].id)_$(id)[label=$(subgraph_factors[1]), style=filled, fillcolor=lavender]\n" 
+        factor_str = "factor$(subgraphs[1].id)_$(id)[label=$(subgraph_factors[1]), style=filled, fillcolor=lavender]\n"
         subg_str = "g$(subgraphs[1].id)_$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
         node_temp *= factor_str * subg_str
         arrow_temp *= "factor$(subgraphs[1].id)_$(id)->g$(subgraphs[1].id)_$(id)[arrowhead=vee,]\ng$(subgraphs[1].id)->g$(subgraphs[1].id)_$(id)[arrowhead=vee,]\n"
@@ -98,14 +98,14 @@ function to_dotstatic(::Type{ComputationalGraphs.Power{N}}, id::Int, factor::F,
     return node_temp, arrow_temp
 end
 
-function to_dotstatic(::Type{ComputationalGraphs.Sum},  id::Int, factor::F,subgraphs::Vector{FeynmanGraph{F,W}}, subgraph_factors::Vector{F}) where {F,W}
+function to_dotstatic(::Type{ComputationalGraphs.Sum}, id::Int, factor::F, subgraphs::Vector{FeynmanGraph{F,W}}, subgraph_factors::Vector{F}) where {F,W}
     node_temp = ""
     arrow_temp = ""
     if factor != 1
         opr_fac = "factor$(id)[label=$(factor), style=filled, fillcolor=lavender]\n"
-        opr_name =  "g$(id)_t"
-        node_str  = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
-        arrow_temp*= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
+        opr_name = "g$(id)_t"
+        node_str = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
+        arrow_temp *= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
         node_temp *= opr_fac * node_str
     else
         opr_name = "g$id"
@@ -123,7 +123,7 @@ function to_dotstatic(::Type{ComputationalGraphs.Sum},  id::Int, factor::F,subgr
             arrow_temp *= "g$(g.id)->$opr_name[arrowhead=vee,]\n"
         end
     end
-    return node_temp,arrow_temp
+    return node_temp, arrow_temp
 end
 
 function to_dotstatic(::Type{ComputationalGraphs.Prod}, id::Int, factor::F, subgraphs::Vector{FeynmanGraph{F,W}}, subgraph_factors::Vector{F}) where {F,W}
@@ -131,20 +131,20 @@ function to_dotstatic(::Type{ComputationalGraphs.Prod}, id::Int, factor::F, subg
     arrow_temp = ""
     if factor != 1
         opr_fac = "factor$(id)[label=$(factor), style=filled, fillcolor=lavender]\n"
-        opr_name =  "g$(id)_t"
-        node_str  = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
-        arrow_temp*= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
+        opr_name = "g$(id)_t"
+        node_str = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
+        arrow_temp *= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
         node_temp *= opr_fac * node_str
     else
         opr_name = "g$id"
     end
-    opr_node  = opr_name * "[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n" 
+    opr_node = opr_name * "[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
     node_temp *= opr_node
     if length(subgraphs) == 1
-        if subgraph_factors[1] ==1
+        if subgraph_factors[1] == 1
             arrow_temp *= "g$(subgraphs[1].id)->$opr_name[arrowhead=vee,]\n"
         else
-            factor_str = "factor$(subgraphs[1].id)_$(id)[label=$(subgraph_factors[1]), style=filled, fillcolor=lavender]\n" 
+            factor_str = "factor$(subgraphs[1].id)_$(id)[label=$(subgraph_factors[1]), style=filled, fillcolor=lavender]\n"
             node_temp *= factor_str
             arrow_temp *= "factor$(subgraphs[1].id)_$(id)->$opr_name[arrowhead=vee,]\ng$(subgraphs[1].id)->$opr_name[arrowhead=vee,]\n"
         end
@@ -161,7 +161,7 @@ function to_dotstatic(::Type{ComputationalGraphs.Prod}, id::Int, factor::F, subg
             end
         end
     end
-    return node_temp,arrow_temp
+    return node_temp, arrow_temp
 end
 
 function to_dotstatic(::Type{ComputationalGraphs.Power{N}}, id::Int, factor::F, subgraphs::Vector{FeynmanGraph{F,W}}, subgraph_factors::Vector{F}) where {N,F,W}
@@ -169,19 +169,19 @@ function to_dotstatic(::Type{ComputationalGraphs.Power{N}}, id::Int, factor::F,
     arrow_temp = ""
     if factor != 1
         opr_fac = "factor$(id)[label=$(factor), style=filled, fillcolor=lavender]\n"
-        opr_name =  "g$(id)_t"
-        node_str  = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
-        arrow_temp*= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
+        opr_name = "g$(id)_t"
+        node_str = "g$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
+        arrow_temp *= "factor$(id)->g$(id)[arrowhead=vee,]\ng$(id)_t->g$(id)[arrowhead=vee,]\n"
         node_temp *= opr_fac * node_str
     else
         opr_name = "g$id"
     end
-    opr_node  = opr_name * "[shape=box, label = \"Pow\", style=filled, fillcolor=darkolivegreen,]\n" 
+    opr_node = opr_name * "[shape=box, label = \"Pow\", style=filled, fillcolor=darkolivegreen,]\n"
     order_node = "order$(id)[label=$N, style=filled, fillcolor=lavender]\n"
     node_temp *= opr_node * order_node
-    arrow_temp*= "order$(id)->$opr_name[arrowhead=vee,]\n"
+    arrow_temp *= "order$(id)->$opr_name[arrowhead=vee,]\n"
     if subgraph_factors[1] != 1
-        factor_str = "factor$(subgraphs[1].id)_$(id)[label=$(subgraph_factors[1]), style=filled, fillcolor=lavender]\n" 
+        factor_str = "factor$(subgraphs[1].id)_$(id)[label=$(subgraph_factors[1]), style=filled, fillcolor=lavender]\n"
         subg_str = "g$(subgraphs[1].id)_$(id)[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
         node_temp *= factor_str * subg_str
         arrow_temp *= "factor$(subgraphs[1].id)_$(id)->g$(subgraphs[1].id)_$(id)[arrowhead=vee,]\ng$(subgraphs[1].id)->g$(subgraphs[1].id)_$(id)[arrowhead=vee,]\n"
@@ -193,13 +193,15 @@ function to_dotstatic(::Type{ComputationalGraphs.Power{N}}, id::Int, factor::F,
 end
 
 """
-    function to_dot_str(graphs::AbstractVector{<:AbstractGraph})
+    function to_dot_str(graphs::AbstractVector{<:AbstractGraph}, name::String="", diagram_id_map=nothing)
+
     Compile a list of graphs into a string for dot language.
+
     # Arguments:
     - `graphs`  vector of computational graphs
-    - `title`   The name of the complied function (defaults to `"ComputationalGraph"`)
+    - `title`   The name of the compiled function (defaults to nothing)
 """
-function to_dot_str(graphs::AbstractVector{<:AbstractGraph}, name::String="ComputationalGraph")
+function to_dot_str(graphs::AbstractVector{<:AbstractGraph}, name::String="", diagram_id_map=nothing)
     head = "digraph ComputationalGraph { \nlabel=\"$name\"\n"
     head *= "ReturnNode[shape=box, label = \"Return\", style=filled, fillcolor=darkorange,]\n"
     body_node = ""
@@ -218,12 +220,12 @@ function to_dot_str(graphs::AbstractVector{<:AbstractGraph}, name::String="Compu
             end
             if isempty(subgraphs(g)) #leaf
                 g_id in inds_visitedleaf && continue
-                leafname = getname(g.properties, leafidx)
+                leafname = get_leafname(g, leafidx, diagram_id_map)
                 if factor(g) == 1
                     gnode_str = "g$g_id[label=$leafname, style=filled, fillcolor=paleturquoise]\n"
                     body_node *= gnode_str
                 else
-                    factor_str = "factor$(leafidx)_inp[label=$(factor(g)), style=filled, fillcolor=lavender]\n" 
+                    factor_str = "factor$(leafidx)_inp[label=$(factor(g)), style=filled, fillcolor=lavender]\n"
                     leaf_node = "l$(leafidx)[label=$leafname, style=filled, fillcolor=paleturquoise]\n"
                     gnode_str = "g$g_id[shape=box, label = \"Mul\", style=filled, fillcolor=cornsilk,]\n"
                     body_node *= factor_str * leaf_node * gnode_str
@@ -233,14 +235,14 @@ function to_dot_str(graphs::AbstractVector{<:AbstractGraph}, name::String="Compu
                 push!(inds_visitedleaf, g_id)
             else
                 g_id in inds_visitednode && continue
-                temp_node,temp_arrow = to_dotstatic(operator(g), g_id, factor(g), subgraphs(g), subgraph_factors(g))
-                body_node *=temp_node
+                temp_node, temp_arrow = to_dotstatic(operator(g), g_id, factor(g), subgraphs(g), subgraph_factors(g))
+                body_node *= temp_node
                 body_arrow *= temp_arrow
                 push!(inds_visitednode, g_id)
             end
             if isroot
                 body_arrow *= "g$(g_id)->ReturnNode[arrowhead=vee,]\n"
-                rootidx +=1
+                rootidx += 1
             end
         end
     end
@@ -250,25 +252,42 @@ function to_dot_str(graphs::AbstractVector{<:AbstractGraph}, name::String="Compu
     return expr
 end
 
-function compile_dot(graphs::AbstractVector{<:AbstractGraph}, filename::String; graph_name="ComputationalGraph")
-    dot_string = to_dot_str(graphs, graph_name)
+function compile_dot(graphs::AbstractVector{<:AbstractGraph}, filename::String; graph_name="", diagram_id_map=nothing)
+    dot_string = to_dot_str(graphs, graph_name, diagram_id_map)
     open(filename, "w") do f
         write(f, dot_string)
     end
 end
 
-function getname(properties,leafidx)
-    if properties isa BareGreenId
-        lfname = "<<i>G</i><sub>$leafidx</sub>>"
-    elseif properties isa BareInteractionId
-        lfname = "<<i>V</i><sub>$leafidx</sub>>"
-    elseif typeof(properties) == FeynmanProperties && properties.diagtype == ComputationalGraphs.Propagator
-        lfname = "<<i>G</i><sub>$leafidx</sub>>"
-    elseif typeof(properties) == FeynmanProperties && properties.diagtype == ComputationalGraphs.Interaction
-        lfname = "<<i>V</i><sub>$leafidx</sub>>"
+function get_leafname(g, leafidx, diagram_id_map=nothing)
+    println(typeof(g))
+    leaftype = Nothing
+    if g isa FeynmanGraph
+        leaftype = g.properties.diagtype
+    elseif g isa Graph
+        if isnothing(diagram_id_map) == false
+            leaftype = typeof(diagram_id_map[g.id])
+        end
+    else
+        error("Unknown graph type: $(typeof(g))")
+    end
+    if leaftype in [BareGreenId, ComputationalGraphs.Propagator]
+        leafname = "<<i>G</i><sub>$leafidx</sub>>"
+    elseif leaftype in [BareInteractionId, ComputationalGraphs.Interaction]
+        leafname = "<<i>V</i><sub>$leafidx</sub>>"
+    elseif leaftype == PolarId
+        leafname = "<&Pi;<sub>$leafidx</sub>>"
+    elseif leaftype == Ver3Id
+        leafname = "<&Gamma;<sup>(3)</sup><sub>$leafidx</sub>>"
+    elseif leaftype == Ver4Id
+        leafname = "<&Gamma;<sup>(4)</sup><sub>$leafidx</sub>>"
     else
-        lfname = "<L<sub>$leafidx</sub>>"
+        leafname = "<L<sub>$leafidx</sub>>"
     end
-    return lfname
+    println()
+    println(g)
+    println(leaftype)
+    println(leafname)
+    println()
+    return leafname
 end
-
diff --git a/src/computational_graph/transform.jl b/src/computational_graph/transform.jl
index ee3ba934..fecf791a 100644
--- a/src/computational_graph/transform.jl
+++ b/src/computational_graph/transform.jl
@@ -183,7 +183,7 @@ end
     function flatten_chains(g::AbstractGraph) 
 
     Recursively flattens chains of subgraphs within a given graph `g` by merging certain trivial unary subgraphs into their parent graphs,
-    This function returns a new graph with flatten chains, dervied from the input graph `g` remaining unchanged.
+    This function returns a new graph with flatten chains, derived from the input graph `g` remaining unchanged.
 
 # Arguments:
 - `g::AbstractGraph`: graph to be modified