Total irregularity of fractal graphs

BERBERLER Z. N.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, cilt.15, sa.07, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 07
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1142/s1793557122501352
  • Dergi Adı: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Anahtar Kelimeler: Irregularity, total irregularity, degree sequence, fractal graph, graph operations, ZAGREB INDEXES
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

The irregularity of a simple undirected graph G is defined as irr(G) = Sigma(uv is an element of E(G)) vertical bar d(G)(u) - d(G) (v) vertical bar, where d(G) (u) denotes the degree of a vertex u is an element of V (G). The total irregularity of a graph as a new measure of graph irregularity is defined as irr(t) (G) = 1/2 Sigma(u,v is an element of V (G) )vertical bar d(G) (u) - d(G) (v) vertical bar. In this paper, the irregularity and the total irregularity of fractal graphs and the derived graphs from a class of fractal graphs are investigated. Exact formulae are presented for the computation of the irregularity and total irregularity of fractal-type graphs in terms of the parameters of the underlying graphs.