Nature

Graph Polynomials and Duality in Graph Theory

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 ...
IEEE

Weighted graph characteristics from oriented line graph polynomials

Abstract: We develop a novel method for extracting graph characteristics from edge-weighted graphs, based on an extension of the Ihara zeta function from unweighted to edge-weighted graphs. This is ...
acm.org

From Polynomial Time Queries to Graph Structure Theory

Download PDF Join the Discussion View in the ACM Digital Library EXAMPLE 2. A standard way of representing graphs is by their adjacency matrices; once we have an adjacency matrix we can obtain a {0, 1 ...
IEEE

Capturing Polynomial Time on Interval Graphs

Abstract: We prove a characterization of all polynomial-time computable queries on the class of interval graphs by sentences of fixed-point logic with counting. More precisely, it is shown that on the ...
Scientific Research Publishing

Wu, T., Feng, L. and Ma, H. (2016) On the Characteristic Polynomials of Graphs with Nullity n - 4. Acta Scientiarum Naturalium Universitatis Sunyatseni, 55, 57-63.

ABSTRACT: Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all ...