The number of maximal cliques and spectral radius of graphs with certain forbidden subgraphs

Abstract

Turán theorem states that the Turán graph [Formula: see text] is the unique graph which has the maximum edge number among the [Formula: see text]-free graphs of order [Formula: see text]. In this paper, we prove that [Formula: see text] has both the maximum number of maximal cliques and the maximum spectral radius among all graphs of order [Formula: see text] with [Formula: see text] and [Formula: see text], where [Formula: see text] stands for the maximum number of disjoint [Formula: see text]cliques of [Formula: see text].