On graphs with diameter 2

Abstract

Consider the set of those graphs with p points in which whenever two points are not joined by a line then there are at least k points joined to both of them. We prove that if p≥2k then among these graphs there is exactly one with minimal number of lines, the complete graph with k points in one class. This extends a result of Murty and Vijayam. © 1976 Academic Press, Inc.

Publication Title

Journal of Combinatorial Theory, Series B

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