Sombor Indices of Some Graphs
Sebina Mathew C *
Department of Mathematics, All Saints’ College, Thiruvanathapuram & NSS Hindu College, Changanassery, Kottayam, India.
Satheesh E.N
Department of Mathematics, NSS Hindu College, Changanassery, Kottayam, India.
*Author to whom correspondence should be addressed.
Abstract
Let G be a graph with no loops and parallel edges. The Sombor index SO(G) of graph G was introduced recently by I. Gutman and defined as SO = SO(G) =\(\sum\)ij∈E(G) \(\sqrt{d^2_i+d^2_j}\) where the degree of the vertex i in G is denoted by di. Graph operations such as Subdivision, concept of Triangular graph, Semi Total graph and Total graph are used to derive complex graphs from the pre-existing simple graph. The study of the topological indices of these graph operations help in identifying the structural properties of complex graph in specific areas like computer, chemical and biological sciences. In this paper, we calculate the Sombor index of Subdivisions of Graph S(G), Triangle Parallel Graph R(G), Semi Total graph Q(G) and the Total graph T(G) of a few classes of graph G.
Keywords: Topological indices, operations on graph, sombor Index