中文

Operations Research Transactions >

2024 , Vol. 28 >Issue 1: 141 - 152

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2024.01.012

The sharp bounds on general sum-connectivity index of graphs for operations based on strong product

Expand
  • 1. School of Mathematics, East China University of Science and Technology, Shanghai 200237, China

Received date: 2020-12-24

  Online published: 2024-03-16

Copyright

, 2024, All rights reserved, without authorization
Fold

Abstract

For a graph $G$, the edge set of graph $G$ denoted by $E(G)$, the vertex set of graph $G$ denoted by $V(G)$, let $d_G (v)$ denote the degree of $v$. For an edge $e=uv$, the general sum-connectivity index $\chi_\alpha(e)=(d_G(u)+d_G(v))^\alpha$, in which $\alpha$ is any real number. In current paper, we introduce firstly the four operations($S, R, Q, T$) of the graph, then give the strong product under the four operations, and determine the upper and lower bounds of the general sum-connectivity index of the four graphs by using the maximum and minimum degrees.

Key words： general sum-connectivity index; strong product; four new operations; F-sum

Cite this article

Zhihao LI, Yan ZHU . The sharp bounds on general sum-connectivity index of graphs for operations based on strong product[J]. Operations Research Transactions, 2024 , 28(1) : 141 -152 . DOI: 10.15960/j.cnki.issn.1007-6093.2024.01.012

References

1 Wiener H . Structural determination of paraffin boiling points[J]. Journal of the American Chemical Society, 1947, 69 (1): 17- 20.
2 Gutman I , Trinajsti? N . Graph theory and molecular orbitals, total $\pi$-electron energy of alternant hydrocarbons[J]. Chemical Physics Letters, 1972, 17 (4): 535- 538.
3 Deng H , Sarala D , Ayyaswamy S K , et al. The Zagreb indices of four operations on graphs[J]. Applied Mathematics and Computation, 2016, 275, 422- 431.
4 Li X , Zheng J . A unified approach to the extremal trees for different indices[J]. Match Communications in Mathematical & in Computer Chemistry, 2005, 54, 195- 208.
5 Zhou B , Trinajsti? N . On a novel connectivity index[J]. Journal of Mathematical Chemistry, 2009, 46, 1252- 1270.
6 Zhou B , Trinajsti? N . On general sum-connectivity index[J]. Journal of Mathematical Chemistry, 2010, 47, 210- 218.
7 秦倩楠, 邵燕灵. 三圈图的极小广义和连通指数[J]. 运筹学学报, 2018, 22 (1): 142- 150.
8 Cvetkovic D M , Doob M , Sachs H . Spectra of Graphs: Theory and Applications[M]. New York: Academic, 1980.
9 Yan W , Yang B Y , Yeh Y N . The behavior of Wiener indices and polynomials of graphs under five graph decorations[J]. Applied Mathematics Letters, 2007, 20, 290- 295.
10 Eliasi M , Taeri B . Four new sums of graphs and their Wiener indices[J]. Discrete Applied Mathematics, 2009, 157 (4): 794- 803.
11 De N , Nayeem S M A , Pal A . F-index of some graph operations[J]. Discrete Mathematics Algorithms and Applications, 2016, 8 (2): 1650025- 1650025.
12 Onagh B N . The harmonic index of graphs based on some operations related to the lexicographic product[J]. Mathematical Sciences, 2019, 13, 165- 174.
13 Akhter S , Imran M . The sharp bounds on general sum-connectivity index of four operations on graphs[J]. Journal of Inequalities and Applications, 2016, 2016, 241.
14 Ahmad M , Saeed M , Javaid M , et al. Exact formula and improved bounds for general sum-connectivity index of graph-operations[J]. IEEE Access, 2019, 167290- 167299.
15 Du Z , Zhou B , Trinajsti? N . Minimum general sum-connectivity index of unicyclic graphs[J]. Journal of Mathematical Chemistry, 2010, 48, 697- 703.
16 Tache R M . General sum-connectivity index with $\alpha\geq-1$ for bicyclic graphs[J]. Match Communications in Mathematical and in Computer Chemistry, 2014, 72, 761- 774.
17 Tomescua I , Kanwal S . Ordering trees having small general sum-connectivity index[J]. Match Communications in Mathematical and in Computer Chemistry, 2013, 69, 535- 548.
Options
Outlines

/

〈 〉