Enumeration of nonisomorphic interval graphs and nonisomorphic permutation graphs

Counting with Symmetry : Polya - Redfield Enumeration of Nonisomorphic Graphs

Topology is the subfield of mathematics that is concerned with the study of shape. Mathematicians have studied topological questions for the past 250 years. However, in just the past 15 years topology has been found to have many different applications to real world problems. One of these is to use a topological tool called persistence homology to understand and analyze high dimensional and comp...

Isomorphic Cayley graphs on nonisomorphic groups

The issue of when two Cayley digraphs on different abelian groups of prime power order can be isomorphic is examined. This had previously been determined by Anne Joseph for squares of primes; her results are extended.

Isomorphic and Nonisomorphic, Isospectral Circulant Graphs

New criteria for which Cayley graphs of cyclic groups of any order can be completely determined–up to isomorphism–by the eigenvalues of their adjacency matrices is presented. Secondly, a new construction for pairs of nonisomorphic Cayley graphs of cyclic groups with the same list of eigenvalues of their adjacency matrices will be presented.

Graphs with all spanning trees nonisomorphic

Nonexistence of Triples of Nonisomorphic Connected Graphs with Isomorphic Connected P3-graphs

In the paper “Broersma and Hoede, Path graphs, J. Graph Theory 13 (1989) 427-444”, the authors asked a problem whether there is a triple of mutually nonisomorphic connected graphs which have an isomorphic connected P3-graph. In this paper, we show that there is no such triple, and thus completely solve this problem.