Differential in infrastructure networks

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Kanli A., BERBERLER Z. N.

RAIRO-OPERATIONS RESEARCH, vol.55, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55
  • Publication Date: 2021
  • Doi Number: 10.1051/ro/2020032
  • Journal Name: RAIRO-OPERATIONS RESEARCH
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Business Source Elite, Business Source Premier, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Differential, domination, graph invariant
  • Dokuz Eylül University Affiliated: Yes

Abstract

Let G = (V, E) be a graph of order n and let B(D) be the set of vertices in V \ D that have a neighbor in the vertex set D. The differential of a vertex set D is defined as partial differential (D) = |B(D)| - |D| and the maximum value of partial differential (D) for any subset D of V is the differential of G. A set D of vertices of a graph G is said to be a dominating set if every vertex in V \ D is adjacent to a vertex in D. G is a dominant differential graph if it contains a partial differential -set which is also a dominating set. This paper is devoted to the computation of differential of wheel, cycle and path-related graphs as infrastructure networks. Furthermore, dominant differential wheel, cycle and path-related types of networks are recognized.