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Keywords
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Deza graph, Eigenvalues, Strongly regular graph, Divisible design graph, Distance-regular graph, Cospectral graphs.
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Abstract
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A Deza graph G with parameters (n,k,b,a) is a k-regular graph with n vertices such that any two distinct vertices have b or a common neighbours. The children G A and G B of a Deza graph G are defined on the vertex set of G such that every two distinct vertices are adjacent in G A or G B if and only if they have a or b common neighbours, respectively. A strongly Deza graph is a Deza graph with strongly regular children. In this paper we give a spectral characterisation of strongly Deza graphs, show relationships between eigenvalues, and study strongly Deza graphs which are distance-regular.
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