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On marker set distance cospectral graphs

Medha Itagi Huilgol

Abstract

Let G = (V ,E) be a simple undirected connected graph and let M be a nonempty subset of vertices of G. Using the results we have derived in our previous paper on marker set distance matrix, we define two graphs G1 with a marker set M1 and G2 with a marker set M2 to be marker set cospectral if they have the same marker distance spectrum. In this paper, we obtain the conditions under which two graphs are marker set cospectral. Algorithms are developed for the same. The polynomials which can be realised as the characteristic polynomial of a M-set distance matrix and real numbers which can be realised as the eigenvalues of a M-set distance are also discussed. AMS subject classification: Primary 05C12, 05C50, 92E10.

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