Quadratic embedding constants of hairy cycle graphs

Abstract

The quadratic embedding (QE) class of the connected graph G = (V, E) is determined based on its quadratic embedding constant (QEC) of the distance matrix graph G. The distance matrix is a conditionally definite negative, or equivalently if it admits a quadratic embedding in a Hilbert space, or if QEC of the graph G is non-positive. In this study, the classification for the hairy cycle graphs such as bearded cycle graph BC (k,m) for k is even, bearded cycle graph BC (3,m) and broken sun graph BC (4,m) will be calculated, and we derive the formulae of its QEC. These classes of graphs belongs to the QE class.