Construction of non-regular A_α-cospectral graphs from some join of graphs

2022/10/13 by K, Najiya V, A, Chithra
#05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.06715

Abstract

Cospectral graphs are a fascinating concept in graph theory, where two non-isomorphic graphs possess identical sets of eigenvalues. In this paper, we compute the A_α-characteristic polynomial of neighbour and non-neighbour splitting join, neighbour and non-neighbour shadow join, central vertex and edge join and duplicate join of two graphs. In addition, when \graphene₁ and \graphene₂ are regular, we compute the A_α-spectrum of these graphs. As an application, we construct non-regular, non-isomorphic graphs that are A_α-cospectral.

Related

• New constructions of non-regular cospectral graphs
• Constructions of A_α-cospectral graphs using some corona operations
• Constructing Families of Cospectral Regular Graphs
• Characterizing cospectral vertices via isospectral reduction
• On the A_α-spectra of some join graphs