Sombor Index over the Tensor and Cartesian Products of Monogenic Semigroup Graphs


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OĞUZ ÜNAL S.

SYMMETRY-BASEL, vol.14, no.5, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.3390/sym14051071
  • Journal Name: SYMMETRY-BASEL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: monogenic semigroups, graphs, tensor product, Cartesian product, indices, ZERO-DIVISOR GRAPH, TOPOLOGICAL INDEXES, WIENER INDEX
  • Sivas Cumhuriyet University Affiliated: Yes

Abstract

Consider a simple graph G with vertex set V(G) and edge set E(G). A graph invariant for G is a number related to the structure of G, which is invariant under the symmetry of G. The Sombor index of G is a new graph invariant defined as SO(G)=SO(G) = Sigma uv is an element of E(G)root(d(u))(2)Op + (d(v))(2) + (d(v))(2). In this work, we connected the theory of the Sombor index with abstract algebra. We computed this topological index over the tensor and Cartesian products of a monogenic semigroup graph by presenting two different algorithms; the obtained results are illustrated by examples.