SYMMETRY-BASEL, vol.14, no.5, 2022 (SCI-Expanded)
Article / Article
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
monogenic semigroups, graphs, tensor product, Cartesian product, indices, ZERO-DIVISOR GRAPH, TOPOLOGICAL INDEXES, WIENER INDEX
Sivas Cumhuriyet University Affiliated:
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.