An explicit formula for the harmonic indices and harmonic polynomials of carbon nanocones CNCk[n]

Sardar M. S., Xu S., Sajjad W., Zafar S., Cangül İ. N., Farahani M. R.

JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES, vol.41, pp.879-890, 2020 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 41
  • Publication Date: 2020
  • Doi Number: 10.1080/02522667.2020.1753304
  • Journal Name: JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.879-890
  • Keywords: Molecular graphs, Carbon nanocones CNCk[n], Harmonic index, Harmonic polynomial, CIRCUMCORONENE SERIES, GRAPHS, FAMILY, OMEGA
  • Bursa Uludag University Affiliated: Yes

Abstract

Let G be a simple molecular graph without directed and multiple edges and without loops. The vertex and edge-sets of G are denoted by V(G) and E(G), respectively. Suppose G is also a connected molecular graph and let u, v is an element of V(G) be two vertices. The harmonic index H(G) of G is defined as the sum of the weights 2(d(u)+d(v))(-1) of all edges in E(G), where d(v) is the degree of a vertex v in G which is defined as the number of vertices of G adjacent to v. The harmonic polynomial of G is defined as H(G, x) = Sigma(e=uv is an element of E(G)) 2x((du+dv-1)) and there is the following nice relation between these two notions H(G) = integral(1)(0) H(G, x)dx. In this paper, we present an explicit formula for the harmonic indices and harmonic polynomials of carbon nanocones CNCk[n].