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

作者：Carvalho Paula^*

来源：Electronic Journal of Linear Algebra, 2012, 25: 3-8.

• Graph theory
• Graph spectra
• Integral graphs
• Strongly regular graphs
• Dominating sets

A subset of the vertex set of a graph G, S subset of V (G), is a (k, tau)-regular set if it induces a k-regular subgraph of G and every vertex not in the subset has tau neighbors in it. This paper is a contribution to the given problem of existence of (k, tau)- regular sets associated with all distinct eigenvalues of integral strongly regular graphs. The minimal idempotents of the Bose- Mesner algebra of strongly regular graphs are used to obtain a necessary and sufficient condition on the existence of (k, tau )- regular sets for its two restricted eigenvalues.

• 出版日期2012