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

BERBERLER Z. N.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, vol.37, no.3, pp.747-754, 2019 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 3
  • Publication Date: 2019
  • Journal Name: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Academic Search Premier, Directory of Open Access Journals
  • Page Numbers: pp.747-754
  • Keywords: Irregularity of a graph, total irregularity of a graph, variance of the vertex degrees, Mycielski construction, VARIABLE NEIGHBORHOOD SEARCH, EXTREMAL GRAPHS
  • Dokuz Eylül University Affiliated: Yes

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.