Topological invariants for the triangular graph of even degree vertices and its line graph

Daniel Brito; Edgar Marquez; Felix Rosas; Ennis Rafael Rosas

doi:10.5269/bspm.62697

Daniel Brito Universidad De Oriente https://orcid.org/0000-0002-4925-2976
Edgar Marquez Universidad del Norte https://orcid.org/0000-0002-7503-1528
Felix Rosas Instituto Venezolano de Investigaciones Cientificas
Ennis Rafael Rosas Universidad de la Costa https://orcid.org/0000-0001-8123-9344

Resumo

Graph theory has an important role in the field of computer science, for example, networks of communication; in electronic and electrical engineering, used in, in industrial processes,electronic instrumentation; in chemistry, for example, the studyof molecules and its properties, etc. The triangular graph witheven degree vertices, TGk, associated with a number k 2 Z+is the graph TGk = (V;E) with jV j = n = k(k + 1)=2 andjEj = m = 3k(k 1)=2, k 2 Z+, where k denotes the num-ber of vertices in the base graph. A topological index (TI ) is areal number attached with the networks graph and correlates thechemical networks with many chemical and physical properties. Inthis paper, our aim is to compute the degree-based indices of theTGk and its line graph. In [10], the M-polynomial is defined asM(G; x; y) =Pi j mij(G)xiyj , where G is a graph, x; y 2 V (G)and mij(G); i; j 1 is the number of edges of G. To computedegree-based indices, we firstly computed the M-polynomials andthen from the M-polynomial we recover eleven degree-based topo-logical indices of the TGk and its line graph.

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Biografia do Autor

Felix Rosas, Instituto Venezolano de Investigaciones Cientificas

Laboratorio de Fisicoquimica Organica

Ennis Rafael Rosas, Universidad de la Costa

Departamento de Ciencias Naturales y Exactas

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