ELA A NOTE ON STRONGLY REGULAR GRAPHS AND (k, τ)-REGULAR SETS

A note on strongly regular graphs and (k,tau)-regular sets

A subset of the vertex set of a graph G, S ⊆ V (G), is a (k, τ)-regular set if it induces a k-regular subgraph of G and every vertex not in the subset has τ neighbors in it. This paper is a contribution to the given problem of existence of (k, τ)-regular sets associated with all distinct eigenvalues of integral strongly regular graphs. The minimal idempotents of the Bose-Mesner algebra of stron...

Ela Strongly Regular Graphs : Values of Λ and Μ For

Dedicated to the memory of Prof. Dom de Caen Abstract. Given λ and μ, it is shown that, unless one of the relations (λ− μ)2 = 4μ, λ− μ = −2, (λ− μ)2 + 2(λ− μ) = 4μ is satisfied, there are only finitely many parameter sets (v, k, λ, μ) for which a strongly regular graph with these parameters could exist. This result is used to prove as special cases a number of results which have appeared in pre...

On Independent Star Sets in Finite Graphs

Let G be a finite graph with μ as an eigenvalue of multiplicity k. A star set for μ is a set X of k vertices in G such that μ is not an eigenvalue of G−X. We investigate independent star sets of largest possible size in a variety of situations. We note connections with symmetric designs, codes, strongly regular graphs, and graphs with least eigenvalue −2. AMS Classification: 05C50

A Note on Strongly Quotient Graphs

Switching of Edges in Strongly Regular Graphs I: A Family of Partial Difference Sets on 100 Vertices

We present 15 new partial difference sets over 4 non-abelian groups of order 100 and 2 new strongly regular graphs with intransitive automorphism groups. The strongly regular graphs and corresponding partial difference sets have the following parameters: (100,22,0,6), (100,36,14,12), (100,45,20,20), (100,44,18,20). The existence of strongly regular graphs with the latter set of parameters was a...