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Spectral Applications of Vertex-Clique Incidence Matrices Associated with a Graph

Author

Listed:
  • Shaun Fallat

    (Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada)

  • Seyed Ahmad Mojallal

    (Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada)

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 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.

Suggested Citation

  • Shaun Fallat & Seyed Ahmad Mojallal, 2023. "Spectral Applications of Vertex-Clique Incidence Matrices Associated with a Graph," Mathematics, MDPI, vol. 11(16), pages 1-26, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3595-:d:1220661
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