Schultz and Modified Schultz Polynomials for Edge – Identification Chain and Ring – for Square Graphs
Main Article Content
Abstract
In a connected graph , the distance function between each pair of two vertices from a set vertex is the shortest distance between them and the vertex degree denoted by is the number of edges which are incident to the vertex The Schultz and modified Schultz polynomials of are have defined as:
respectively, where the summations are taken over all unordered pairs of distinct vertices in and is the distance between and in The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.
Received 24/9/2020, Accepted 9/2/2021, Published Online First 20/11/2021
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
References
Chartrand G, Lesniak L. Graphs and Digraphs, 6th ed., Wadsworth and Brooks / Cole. California; 2016.
Buckley F, Harary F. Distance in Graphs. Addison – Wesley, Longman; 1990.
Ahmed M A, Haitham NM. Schultz and Modified Schultz Polynomials of two Operations Gutman's. IJERSTE. 2017; 6: 68-74.
Ahmed M A, Haitham N M. Schultz and Modified Schultz Polynomials of Some Cog-Special Graphs. OALIBJ. 2019;6:1-13.
Gao W, Farahani MR, Imran M, Kanna MR. Distance-based topological polynomials and indices of friendship graphs. SpringerPlus. 2016; 5:1563, 1-9. DOI 10.1186/s40064-016-3271-5
Rohith R M, Sudev N, Charles D. Modified Chromatic Schultz Polynomial of Some Cycle Related Graphs. Acta Universitatis Matthiae Belii, series Mathematics.2019; 12–31.
Farahaini M R. Hosoya, Schultz Modified Schultz Polynomials and their Topological Indices of Benzene Molecules: First Members of polycyclic Aromatic Hydro Carbons (PAHs). IJCTC. 2013; 1(2): 6-9.
Farahaini M R. Schultz and Modified Schultz Polynomials of Coronene Polycyclic Aromatic Hydro carbons. ILCPA. 2014; 32: 1-10.
Farahani M R, Wang S, Wei G, Bing Wei, Jamil M K. The Hosoya Schultz and Modified Schultz of Class od Dutch Windmill Graph Dn^((m)) , ∀n, m ∈ N & n ≥ 4, m ≥ 2. Communications in Applied Analysis. 2018; 22(1): 43-62.
Halakoo O, Khormali O, Mahmiani A. Bounds for Schultz Index of Pentachains. Digest Journal of Nanomaterials and Biostructures. 2009; 4(4): 687 – 691.
Heydari A. On the Modified Schultz Index of C4C8(S) Nanotubes and Nanotours. Digest Journal of Nanomatrial and Biostructures. 2010; 5: 51-56.
Schultz HP. Topological organic chemistry 1. Graph theory and topological indices of alkanes. J. Chem. Inf. Comput. Sci. 1989; 29: 227–228.
Klavžar S, Gutman I. Wiener number of vertex-weighted graphs and a chemical application. Disc. Appl. Math. 1997; 80: 73–81.
Haneen K A. Schultz index, Modified Schultz index, Schultz polynomial and Modified Schultz polynomial of alkanes. GJPAM. 2017; 13(9): 5827-5850.
Hassani G, Iranmanesh A, Mirzaie S. Schultz and Modified Schultz Polynomials of C100 Fullerene. MATCH Commun. Math. Comput. Chem. 2013; 69: 87-92.
Iranmanesh A, Ali zadeh Y. Computing Szeged and Schultz Indices of HAC3C7C9[p,q] Nanotube by Gap program. Digest Biostructures. 2009; 4: 67-72.
Ghorbani M, Dehmer M, Mowshowitz A, Tao J, Emmert-Streib F. The Hosoya Entropy of Graphs Revisited. Symmetry. 2019; 11:1-14.
Guo H, Zhow B. Properties of Degree Distance and Gutman Index of Uniform Hypergraphs. MATCH Commun. Math. Comput Chem. 2017; 78: 213-220.
Sadeghieh A, Alikhani S, Ghanbari N, Khalaf A. Hosoya polynomial of some cactus chains. Cogent Mathematics. 2017; 1-7.