A generalization of Fiedler's lemma and the spectra of H-join of graphs

TL;DR

This paper introduces a new generalization of Fiedler's lemma using the main function of a matrix, enabling the derivation of spectra for various graph operations including H-join, generalized join, and corona.

Contribution

It presents a novel generalization of Fiedler's lemma and derives spectra for complex graph operations involving non-regular graphs.

Findings

Spectra of H-join graphs are characterized.

Spectra of H-generalized join graphs are obtained.

Spectra of generalized corona graphs are derived.

Abstract

A new generalization of Fiedler's lemma is obtained by introducing the concept of the main function of a matrix. As applications, the universal spectra of the H-join, the spectra of the H-generalized join and the spectra of the generalized corona of any graphs (possibly non-regular) are obtained.