Matrix Representations of Graphs and Their Experimental Comparison for Detecting Non-subgraphs by Eigenvalues

Abstract

Eigenvalues of graphs have been used for detecting non-subgraphs or non-supergraphs based on their interlacing property. However the detected subgraphs are often restricted to induced subgraphs or trees due to their matrix representations. We consider five matrix representations of a graph, which can be used to detect general non-subgraphs or non-supergraphs, and compare them experimentally.