The Saturation Number of Kp ∪ P3

Abstract

For a given graph [Formula: see text], we call a graph [Formula: see text] as [Formula: see text]-saturated if it contains no [Formula: see text]-copy, but adding any edge of [Formula: see text] creates a subgraph isomorphic to [Formula: see text]. The saturation number, denoted by [Formula: see text], is the minimum size of an [Formula: see text]-saturated graph of order [Formula: see text]. In this paper, we will show the value of [Formula: see text] for [Formula: see text] and [Formula: see text], and give a complete characterization of the extremal graphs.