Abstract
Graph theory is one of the rising areas in mathematics due to its applications in many areas of science. Amongst several study areas in graph theory, spectral graph theory and topological descriptors are in front rows. These descriptors are widely used in QSPR/QSAR studies in mathematical chemistry. Vertex-semitotal graphs are one of the derived graph classes which are useful in calculating several physico-chemical properties of molecular structures by means of molecular graphs modelling the molecules. In this paper, several topological descriptors of vertex-semitotal graphs are calculated. Some new relations on these values are obtained by means of a recently defined graph invariant called omega invariant.
Highlights
Several topological graph indices have been defined and studied by many mathematicians and chemists. They are defined as topological graph invariants measuring several physical, chemical, pharmacological, pharmaceutical, biological, etc. properties of graphs which are modelling real life situations
Two of the most important topological graph indices are called the first and second Zagreb indices denoted by M1(G) and M2(G), respectively: M1(G) =
We obtained the formulae for the topological indices, especially the Zagreb indices and harmonic index, of some class of derived graphs called vertex-semitotal graphs
Summary
Several topological graph indices have been defined and studied by many mathematicians and chemists. We consider degree based-topological indices of some derived graphs through this paper. Let G = (V, E) be a simple graph with | V (G) |= n vertices and | E(G) |= m edges, where V (G) = {v1, v2, · · · , vn} and E(G) = {vivj : vi, vj ∈ V (G)}. The smallest and biggest vertex degrees in a graph will be denoted by δ and ∆, respectively.
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