Displaying similar documents to “Metrically regular square of metrically regular bigraphs. II.”

Metrically regular square of metrically regular bipartite graphs of diameter D = 6

Vladimír Vetchý (1993)

Archivum Mathematicum

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The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only one table of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter D = 6 (7 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter D < 6 see [7] and [8].

Construction of Cospectral Integral Regular Graphs

Ravindra B. Bapat, Masoud Karimi (2017)

Discussiones Mathematicae Graph Theory

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Graphs G and H are called cospectral if they have the same characteristic polynomial. If eigenvalues are integral, then corresponding graphs are called integral graph. In this article we introduce a construction to produce pairs of cospectral integral regular graphs. Generalizing the construction of G4(a, b) and G5(a, b) due to Wang and Sun, we define graphs 𝒢4(G,H) and 𝒢5(G,H) and show that they are cospectral integral regular when G is an integral q-regular graph of order m and H...