DEGREE-BASED INVARIANTS OF MYCIELSKI CONSTRUCTION: IRREGULARITY, TOTAL IRREGULARITY, VARIANCE

Abstract

The degree-based graph invariants are parameters defined by degrees of vertices. A graph is regular if all of its vertices have the same degree. Otherwise a graph is irregular. To measure how irregular a graph is, graph topological indices were proposed including the irregularity of a graph, total irregularity of a graph, and the variance of the vertex degrees. In this paper, the above mentioned irregularity measures for Mycielski constructions of any underlying graph are considered and exact formulae are derived.