@Carl Love I have purchased 2022 research licence today in two days they said I will get the further procedure once done will check and revert back to you sir 200%

Your encouraging is important for my purchase too

@Carl Love by just seeing the code my requirement

A function say 

Let G1 is subgraph of G2 so G1 number of vertices is less than G2

So in L I am going to give a set L from the vertices of G2 so size number the number of  vertices of G1

Now I want to see with the vertices set L which I will input in to the function whether a graph isomorphic to G1 exits in G2 with those labels 

Which vertex is adjacent to which is  are immaterial it is only that does their exists graph of shape G1 in G2 with the vertex labels only in the set L.

IsLabeledIsomorphicSubgraph:= proc(G1::Graph, G2::Graph,L)

@vv The third option with label=true is not their we are looking at such a labeled subgraph Edge adjacencies need not be exact only thing is those set of vertex labels has to be used and that subgraphs edges i require too

A tweek to that code

We could also have funct F(G1,G2, L)

where L is the set whose size is same as number of vertices of G1.

Then we look for G1 in G2 with which has those vertex labels if any such exists it will return those edge set or it will reply false

Remember such a subgraph need not be vertex induced subgraph in it.

If not understood will give an example too both for true and false with very small graph itself

@Carl Love hope I have acknowledged just now

Once I have made some progress or so will come back to you sir on the above problem 

@Carl Love

Please 🙏🙏 take some time to read the below I apologise to distrurb you in your precious time sir

 if possible I used

Step 1: Take the graph G and a graph G1 which we should embed in G with its labels as it is in both cases

Step 2: Let n be number of vertices of G with V as the vertex set. Convert vertex labels of G to { 1,2,3,....,n} for easy purpose.

Step 3: Let G1 be a graph with k vertices say. Vertex set labels converted to {1,2,..k}.

Step 4: Let S= all possible permutations of size k from the n of 

gives us as possible permutations of size k from n vertex labels of G.

Taking all subgraphs G1 with a vertex set labeled with each of those permutations of size k.

Now we need to get a code for IsIsomorphicSubgraph(G,G1) keeping even the labeling of G1 in mind some internal tweek in that program is required like labels= true or false

If labels if labels=true it should take labels also into picture

Kind help if possible

Now we put all these subgraphs into a set or list or any other say S

T= floor(Number of of edges of G/ Number of edges of G1)

Now remove a possible

 edge-disjoint copies of sizeT  from the set S and display them and even may be store them some where

You can even use database if you feel size may be big with large graphs 

Kind help sir this is logic

You can tweek the logic sir with your experience and your efforts of great knowledge please help sir kind help sir 

@Carl Love Kind help sir as per the  lcz 682 comment added it will be very useful to me an mw file with all the relation graph of all the product graphs in one mw file and I can run based on my choice.

Kind help sir.

I use Maple 2020

Kind help possible to get the Relation graph function for all those definations

In a single code of mw file.

Thank you all taking your personal experiences I feel it is better to go for matlab for ML related works 

@Carl Love Error, invalid `$` operator   co-normal.mw  May be because I am using Maple 2020

@Carl Love I a have attached a non-trivial example we need to remove edge-disjoint copies maximum

I have attached the case

Non-trivial_example.mw

non_trivial_example.pdf

maximum number embeddable cases only  of  G's  embeddable into G^k

I need all possible ways with their edges sets in a general G into G^k their could be several ways to get these maximum possible case I want all those cases with the edge sets for each case seperate seperate

If any doubts in this kindly ask I will be greatful to explain

any other details will give

@lcz I require even the edge sets of the edge-disjoint  G1  in G2 and left over edges. in the 3 case which is the maximum number of edge-disjoint G1 in G2 if their are any other ways to get the same number all those ways. In your example taken their is only one maximum way.

In my program is just giving first red part and leaving it has to give full packing properly using the current technologies it should be better i feel i had coded it very back and i have forgotten things of those days

please please kind help

@lcz 

This a video link

https://www.youtube.com/watch?v=BiLjdZYj_RI

Copy paste the above link in browser and check the above youtube video

Sometimes after find the maximum number of ways to get the G1 in G2 its union may not be G2

Then it will have some left over edges then I want the graph formed by left over edges in G2.

If not getting the definetion will send more examples if asked

I am asking for all the subgraphs to be isomorphic to a graph G1 in this code 

But is not required in general you can get it from the youtube link if required more details will give

An H-packing of a graph F is a set P = {H_1,H_2, . . . ,H_t} of edge-disjoint subgraphs of F,
where each subgraph H_i is isomorphic to H.

In packing some left over edges will be their as union will not the entire graph even after maximum number of ways is taken.

F has an H-decomposition if it has an H-packing  with the property that every edge of F appears in exactly one member of the H-packing. This fact is denoted by H|F.

Kind help I will surely acknowledge anyone who can help me

@Carl Love Thank you

Kind help me with my new thread on decomposition of graph with two problems in your free time slowly sir

kind help sir

Theard name "Extract subgraphs from a supergraph"

@Carl Love 

I have a set of edges like this

{{`1:1`,`1:2`},{`1:1`,`2:1`}.........}  like this several may be 300 like this or more those ` quotes are their i just saw i am sorry

so it comes as "`1:1`"  need help for it to be "1:1" type 

i want it to be converted to

{{"1:1","1:2"},{"1:1","2:1"},......}  like inside double qoutes only

kind help

@Carl Love Thank you very much I would like to acknowledge your help really very much