A new approach for constructing graph being determined by their generalized Q-spectrum

2023/11/06 by Gao, Liwen, Guo, Xuejun
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2311.02968

Abstract

Given a graph G, we have the adjacency matrix A(G) and degree diagonal matrix D(G). The Q-spectrum is the all eigenvalues of Q-matrix Q(G)=A(G)+D(G). A class of graphs is determined by their generalized Q-spectrum (DGQS for short) if any two graphs among the class have the same Q-spectrum and so do their complement imply that they are isomorphic. In [11], the authors provides a new way to construct DGQS graphs by considering the rooted product graphs G∘ P_k and they prove when k=2,3, G∘ P_k is DGQS for a special graph G. In this paper, we will prove that under the same conditions for G, the conclusion is true for any positive integer k.

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