On Laplacian integrability of comaximal graphs of commutative rings

The power graph P(Zn) of Zn for a finite cyclic group Zn is a simple undirected connected graph such that two distinct nodes x and y in Zn are adjacent in P(Zn) if and only if x≠y and xi=y or yi=x for some non-negative integer i. In this article, we find the Laplacian eigenvalues of P(Zn) and show that P(Zn) is Laplacian integral (integer algebraic connectivity) if and only if n is either the product of two distinct primes or a prime power. That answers a conjecture by Panda, Graphs and Combinatorics, (2019).

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On Laplacian integrability of comaximal graphs of commutative rings

Cited by 3 publications

References 22 publications

Distance Laplacian spectra of graphs: A survey

Distance Laplacian spectra of graphs: A survey

Linear strand of edge ideals of comaximal graphs of commutative rings

Algebraic Connectivity of Power Graphs of Finite Cyclic Groups

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