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- W4384927394 abstract "In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a vertex-clique incidence matrix for a graph and produce new lower bounds for the negative eigenvalues and negative inertia of a graph. Moreover, utilizing these vertex-clique incidence matrices, we generalize several notions such as the signless Laplacian matrix, and develop bounds on the incidence energy and the signless Laplacian energy of the graph. 
 %The tight upper bounds for the energies of a graph and its line graph are given. 
 More generally, we also consider the set $S(G)$ of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent. An important parameter in this setting is $q(G)$, and is defined to be the minimum number of distinct eigenvalues over all matrices in $S(G)$. For a given graph $G$ the concept of a vertex-clique incidence matrix associated with an edge clique cover is applied to establish several classes of graphs with $q(G)=2$." @default.
- W4384927394 created "2023-07-22" @default.
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- W4384927394 date "2023-07-19" @default.
- W4384927394 modified "2023-10-16" @default.
- W4384927394 title "Spectral Applications of Vertex-Clique Incidence Matrices Associated with a Graph" @default.
- W4384927394 doi "https://doi.org/10.20944/preprints202307.1338.v1" @default.
- W4384927394 hasPublicationYear "2023" @default.
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