# Jernej

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## Registered User

 Name Jernej Member for 3 years Seen 9 hours ago Website Location Slovenia Age 25
Undergrad student interested in extremal aspects of combinatorics/graph theory and theoretical computer science. If you happen to have a neat exercise problem, feel free to post it at http://exwiki.org
 Apr26 awarded ● Nice Question Mar19 comment Good papers/books/essays about the thought process behind mathematical researchThere is also a 41mins long talk by Hamming youtube.com/watch?v=a1zDuOPkMSw if you don't like to read the transcript. Mar14 awarded ● Notable Question Mar12 comment Applications of line graphsDelio, can you cite one of these sociological papers? Mar7 comment Applications of line graphsJust a suggestion. Find a suitable interpretation of vertex/edge colorings. And then play with the fact that the chromatic index of a graph is the chromatic number of its line graph. Feb17 awarded ● Nice Question Feb17 comment Minimal graphs with a prescribed number of spanning treesThe $x$-axis represents $n$ while the $y$ axis represents $\alpha(n)$ Feb11 awarded ● Organizer Feb11 revised determinant of fibonacci-sum graphsedited tags Feb11 comment determinant of fibonacci-sum graphsThe diagonal is of course zero since I am first constructing a graph and then computing the adjacency matrix. Feb11 comment determinant of fibonacci-sum graphsI always get zero with the following sage program for constructing the graph pastebin.com/0t9GHHzM Feb9 comment Mclaughlin GraphWhen I try to run the first example in gap it stops with this error in the first line - Variable: 'AtlasGenerators' must have a value. Do you happen to see why? Feb7 awarded ● Popular Question Feb7 revised Spanning trees in planar graphsdeleted 366 characters in body; deleted 16 characters in body Feb7 comment Spanning trees in planar graphsWeird. I'll try to run the program again and see why the proposed graph is not found. It clearly looks like a counterexample to the stated answer! Feb4 awarded ● Nice Question Feb2 awarded ● Yearling Feb2 awarded ● Yearling Feb1 comment Is the empty graph a tree?@Günter Rote Sage simply computes the subdivision of the Laplacian matrix and its determinant. Feb1 asked Is the empty graph a tree? Jan17 comment Hamiltonian cycles in power-graphsThat's a very nice question! I have tested the conjecture for values of $n$ up to 500 and it holds. Jan17 comment Generating non-isomorphic graphs by adding edges to a given graph@BrendanMcKay the base graph has an automorphism group of order 2^85 * 3^32 * 5^16 * 7^16 Jan16 comment Generating non-isomorphic graphs by adding edges to a given graph@GerhardPaseman A and B are indeed disjoint. And there are no edges between! I don't see any reasons why such a matching would not exists since $B$ is larger then $A.$ Yes, all I really want are nonisomorphic extensions that match $A$ to $B$. BTW, may I ask you about system designs? Jan16 revised Generating non-isomorphic graphs by adding edges to a given graphedited body Jan16 asked Generating non-isomorphic graphs by adding edges to a given graph Jan16 comment Spanning trees in planar graphs@utdiscant In case you haven't noticed the conjecture does not hold! Jan2 awarded ● Popular Question Dec20 comment Similarity measure between 2 bi-partite graph.I suggest you ask this sort of questions on cs.stackexchange.com. As for your question you could use some hybrid function based on the generalized degree sequence of a weighted graph + graph isomorphism + wiener index. But it is hard to give you good suggestions without knowing the full requirements. Dec20 asked Structure of almost all bipartite graphs Dec20 comment Similarity measure between 2 bi-partite graph.I know its irritating but your question is still not well defined. What should the measure say if two graphs have no pair of such vertices but there is some pair where the weights are very close? As such the question is not well defined. Dec20 comment Similarity measure between 2 bi-partite graph.And what exactly should this measure resemble? In what way do you define graph similarity? Dec20 comment Similarity measure between 2 bi-partite graph.It would help if you could specify some additional criterion for your measure. otherwise you could just check for graph isomorphism. Dec15 answered Spanning trees in planar graphs Dec15 comment Counting spanning trees when blowing up verticesHere are the next few values of the number of spanning trees for blowup graphs obtained by taking $K_4$ as a start $$16, 6000, 113906250000, 280568536600470542907714843750000$$ let me know if you want some other values relative to other starting graphs. As for the main question,try to express the adjacency matrix of the blowup graph and see if you can find its eigenvalues in terms of $K_3$ and the base graph. Dec15 comment Counting spanning trees when blowing up verticesWhat exactly is the adjacency among the triangles? If $T_u,T_v$ are triangles that were obtained from two adjacent vertices $u,v$ then every vertex of $T_v$ is adjacent to every vertex of $T_u$? Dec15 comment Counting spanning trees when blowing up verticesSo what you really want is derive an identity for the spectrum of the truncated graph with relation to the spectrum of the original graph. By spectrum I mean the eigenvalues of the adjacency or Laplacian matrix. In this case it does not matter.