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Keywords = vertex-clique incidence matrix

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26 pages, 602 KB  
Article
Spectral Applications of Vertex-Clique Incidence Matrices Associated with a Graph
by Shaun Fallat and Seyed Ahmad Mojallal
Mathematics 2023, 11(16), 3595; https://doi.org/10.3390/math11163595 - 19 Aug 2023
Viewed by 1835
Abstract
Using the notions of clique partitions and edge clique covers of graphs, we consider the corresponding incidence structures. This connection furnishes lower bounds on the negative eigenvalues and their multiplicities associated with the adjacency matrix, bounds on the incidence energy, and on the [...] Read more.
Using the notions of clique partitions and edge clique covers of graphs, we consider the corresponding incidence structures. This connection furnishes lower bounds on the negative eigenvalues and their multiplicities associated with the adjacency matrix, bounds on the incidence energy, and on the signless Laplacian energy for graphs. For the more general and well-studied set S(G) of all real symmetric matrices associated with a graph G, we apply an extended version of an incidence matrix tied to an edge clique cover to establish several classes of graphs that allow two distinct eigenvalues. Full article
(This article belongs to the Special Issue Spectral Graph Theory and the Inverse Eigenvalue Problem of a Graph)
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