Constructions of $A_\alpha$-cospectral graphs using some corona operations

TL;DR

This paper computes the $A_\alpha$-spectra of various corona operations on regular graphs and constructs infinitely many pairs of $A_\alpha$-cospectral graphs, advancing spectral graph theory methods.

Contribution

It introduces formulas for the $A_\alpha$-spectra of total, $Q$-vertex, and $Q$-edge corona graphs of regular graphs, and constructs infinite families of cospectral graphs.

Findings

Derived explicit $A_\alpha$-spectra for corona graphs.

Constructed infinitely many $A_\alpha$-cospectral graph pairs.

Extended spectral analysis to new graph operations.

Abstract

Let $ G_1 \circledast G_2$,$ G_1 \sqcupdot G_2 $ and $ G_1 \sqcupplus G_2$ denote the total corona, $Q$-vertex corona and $Q$-edge corona of two graphs $ G_1$ and $ G_2 $, respectively. In this paper, we compute the $A_\alpha$-spectrum of $ G_1 \circledast G_2$,$ G_1 \sqcupdot G_2 $ and $ G_1 \sqcupplus G_2$ for regular graphs $ G_1$ and $ G_2$. As an application, we construct infinitely many pairs of $A_\alpha$-cospectral graphs.