Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

Let G be a directed graph such that every edge e of G is associated with a positive integer, called the index of e. Then G is called a network graph if, at every vertex v of G, the sum of the indices ...

Well, if I remember my graph theory well enough, if A is the adjacency matrix of the graph, each entry of A^n is the number of ways to get between the corresponding nodes in n steps or less. So, to do ...

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...

Text: : "Graph Theory" by J. Adrian Bondy and U.S.R. Murty; Graduate Texts in Mathematics 244, Springer 2008. ISBN 978-1-84628-969-9, 2nd printing, 978-1-84628-970-5 (ebook). Notes will be supplied ...

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks — vertices (dots) and edges (lines connecting them) — has been an invaluable way ...

Now that pandemic restrictions are easing up, people are getting together again. But it’s been a while, so if you and your friends need some help breaking the ice, here’s a mathematical party game you ...