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Keywords
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Deza graph, Deza children,
divisible design graph,
spectrum of graph, nullity
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Abstract
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A Deza graph with parameters (n, k, b, a) is a k-regular graph with
n vertices such that any two of its vertices have b or a common
neighbours, where b ≥ a. In this paper we investigate spectra of
Deza graphs. In particular, using the eigenvalues of a Deza graph
we determine the eigenvalues of its children. Divisible design graphs
are significant cases of Deza graphs. Sufficient conditions for Deza
graphs to be divisible design graphs are given, a few families of divisible design graphs are presented and their properties are studied. Our special attention goes to the invertibility of the adjacency matrices of
Deza graphs.
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