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Alternative Proofs of a Theorem of Bose and Dowling for Strongly Regular Graphs
Malik Talbi
In this paper, we give two proofs of a theorem of Bose and Dowling on non necessarily regular graphs satisfying the two other conditions of strong regularity. This theorem states that a simple graph for which there exist two non-negative entegers λ and μ such that any two adjacent vertices have exactly λ common neighbors and any two nonadjacent vertices have exactly μ common neighbors, is regular except for some cases that can be considered as trivial.
Keywords: The friendship theorem, strongly regular graphs, regularity, counting in two ways