Adjacency Spectra of Semigraphs
Pralhad M. Shinde
TL;DR
This paper introduces the concept of adjacency matrices for semigraphs, providing conditions for their existence, an algorithm for construction, and analyzing eigenvalues, especially for star semigraphs.
Contribution
It defines semigraph adjacency matrices, establishes construction conditions, and studies their eigenvalues, advancing the spectral theory of semigraphs.
Findings
Derived bounds for largest eigenvalues of semigraph adjacency matrices.
Provided an algorithm to construct semigraphs from semigraphical matrices.
Analyzed eigenvalues of adjacency matrices for specific star semigraphs.
Abstract
In this paper, we define the adjacency matrix of a semigraph. We give the conditions for a matrix to be semigraphical and give an algorithm to construct a semigraph from the semigraphical matrices. We derive lower and upper bounds for largest eigenvalues. We study the eigenvalues of adjacency matrix of two types of star semigraphs.
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Taxonomy
TopicsGraph theory and applications · Graph Theory and Algorithms · Matrix Theory and Algorithms