Original Research Article

Article volume = 2021 and issue = 1

Pages: 1-6

Article publication Date: February 19, 2021

You can download PDF file of the article here: Download

Visited 268 times and downloaded 175 times

# Eccentric Connectivity and Connective Eccentricity Indices of Generalized Petersen Graphs

#### Suleyman Ediza(a), Murat Cancana(a), Mohammad Reza Farahani(b)

(a) Faculty of Education, Van Yuzuncu Yil University, Turkey

(b) Iran University of Science and Technology Tehran, Iran

##### Abstract:

Research on the topological indices based on eccentricity of vertices of a molecular graph has been intensively rising recently. The eccentric connectivity index and the connective eccentricity index are belonging to this class of indices. In this paper we computed the exact value of the eccentric connectivity and the connective eccentricity indices of generalized Petersen graphs.

##### Keywords:

Connective eccentric index, Eccentric connectivity index, Generalized Petersen graphs

##### References:

- [1] V. Sharma, R. Goswami, A.K. Madan, Eccentric connectivity index: a novel highly discriminating topological descriptor for structure-property and structure-activity studies, J. Chem. Inf. Comput. Sci., 37 (1997), 273–282. 1
- [2] S. Sardana, A.K. Madan, Application of graph theory: relationship of molecular connectivity index, Wiener’s index and eccentric connectivity index with diuretic activity, MATCH Commun. Math. Comput. Chem., 43 (2001), 85–98. 1
- [3] S. Gupta, M. Singh, A.K. Madan, Application of graph theory: relationship of eccentric connectivity index and Wiener’s index with anti-inflammatory activity, J. Math. Anal. Appl., 266 (2002), 259–268. 1
- [4] S. Gupta, M. Singh, A.K. Madan, Connective eccentricity index: a novel topological descriptor for predicting biological activity, J. Mol. Graph. Model., 18 (2000), 18–25. 1
- [5] H. Wang, Extremal trees of the eccentric connectivity index , Ars Combin., 122 (2015), 55–64. 1
- [6] Y.B. Venkatakrishnan, S. Balachandran, K. Kannan, On the eccentric connectivity index of generalized thorn graphs, Nat. Acad. Sci. Lett., 38 (2015), 165–168. 1
- [7] K.C. Das, M.J. Nadiafi-Arani, Comparison between the Szeged index and the eccentric connectivity index, Discrete Appl. Math., 186 (2015), 74–86. 1
- [8] A. Ashrafi,M. Saheli, M. Ghorbani, The eccentric connectivity index of nanotubes and nanotori, J. Comput. Appl. Math.,235 (2011), 4561–4566. 1
- [9] M.J. Morgan, S. Mukwembi, H. C. Swart, Extremal regular graphs for the eccentric connectivity index, Quaest. Math., 37 (2014), 374–378. 1
- [10] T. Dosli´c, M. Saheli, Eccentric connectivity index of composite graphs, Util. Math., 95 (2014), 3–22. 1
- [11] J.B. Zhang, Z.Z. Liu, B. Zhou, On the maximal eccentric connectivity indices of graphs, Appl. Math. J. Chinese Univ. Ser. B., 29 (2014), 374–378. 1
- [12] P. Dankelmann, M.J. Morgan, S. Mukwembi, On the eccentric connectivity index and Wiener index of a graph, Quaest. Math., 37 (2014), 39–47. 1
- [13] B. Eskender, E. Vumar, Eccentric connectivity index and eccentric distance sum of some graph operations, Trans. Comb., 2 (2013), 103–111. 1
- [14] H. Hua, K.C. Das, The relationship between the eccentric connectivity index and Zagreb indices, Discrete Appl. Math., 161 (2013), 2480–2491. 1
- [15] J. Zhang, B. Zhou, Z. Liu, On the minimal eccentric connectivity indices of graphs, Discrete Math., 312 (2012), 819–829. 1
- [16] M.J. Morgan, S. Mukwembi, H.C. Swart, A lower bound on the eccentric connectivity index of a graph, Discrete Appl. Math., 160 (2012), 248–258. 1
- [17] G. Yu, L. Feng, On connective eccentricity index of graphs, MATCH Commun. Math. Comput. Chem., 69 (2013), 611–628. 1
- [18] G. Yu, H. Qu, L. Tang, L. Feng, On the connective eccentricity index of trees and unicyclic graphs with given diameter, J. Math. Anal. Appl., 420 (2014), 1776–1786. 1
- [19] K. Xu, K.C. Das, H. Liu, Some extremal results on connective eccentricity index, J. Discrete Appl. Math., 186 (2015), 74–86. 1
- [20] S. Li, L. Zhao, On the extremal total reciprocal edge-eccentricity of trees, J. Math. Anal. Appl., 433 (2016), 587–602. 1
- [21] E. Zhu, Z. Li, Z. Shao, J. Xu, C. Liu, 3-coloring of generalized Petersen graphs, J. Comb. Optim., 31 (2016), 902–911. 1
- [22] H. Wang, X. Xu, Y. Yang, G. Wang, On the domination number of generalized Petersen graphs P(ck,k), Ars Combin., 118 (2015), 33–49. 1
- [23] A. Benini, A. Pasotti, a-labelings of a class of generalized Petersen graphs, Discuss. Math. Graph Theory., 35 (2015), 43–53. 1
- [24] L. Gao, X. Xu, J. Wang, D. Zhu, Y. Yang, The decycling number of generalized Petersen graphs, Discrete Appl. Math., 181 (2015), 297–300. 1
- [25] D. Ferrero, S. Hanusch, Component connectivity of generalized Petersen graphs, Int. J. Comput. Math., 91 (2014), 1940–1963. 1

##### Cite this article as:

- Suleyman Ediza, Murat Cancana, Mohammad Reza Farahani, Eccentric Connectivity and Connective Eccentricity Indices of Generalized Petersen Graphs, Communications in Combinatorics, Cryptography & Computer Science, 2021(1), PP.1-6, 2021
- Export citation to BibTeX