Sum-connectivity index of a graph

doi:10.1007/s11464-015-0470-2

Front. Math. China

2016, Vol. 11

Issue (1) : 47-54 https://doi.org/10.1007/s11464-015-0470-2

RESEARCH ARTICLE

Sum-connectivity index of a graph

Kinkar Ch. DAS^1,^*(

),Sumana DAS²,Bo ZHOU³

1. Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
2. School of Information and Communication Engineering, Sungkyunkwan University,Suwon 440-746, Korea
3. Department of Mathematics, South China Normal University, Guangzhou 510631, China

Download: PDF(101 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

Let G be a simple connected graph, and let di be the degree of its i-th vertex. The sum-connectivity index of the graph G is defined as χ(G)=Σvivj∈E(G)? (di+dj)−1/2. We discuss the effect on χ(G) of inserting an edge into a graph. Moreover, we obtain the relations between sum-connectivity index and Randić index.

Keywords Graph Randićindex sum-connectivity index minimum degree

Corresponding Author(s): Kinkar Ch. DAS

Issue Date: 02 December 2015

Cite this article:

Kinkar Ch. DAS,Sumana DAS,Bo ZHOU. Sum-connectivity index of a graph[J]. Front. Math. China, 2016, 11(1): 47-54.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0470-2
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I1/47

1	Lučić B, Trinajstíc N, Zhou B. Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons, Chem Phys Lett, 2009, 475:146–148 https://doi.org/10.1016/j.cplett.2009.05.022
2	Luˇcíc B,Nikolíc S,Trinajstíc N, Zhou B, Turk S I. Sum-connectivity index. In: Gutman I, Furtula B, eds. Novel Molecular Structure Descriptors—Theory and Applications I. University of Kragujevac, Kragujevac, 2010, 101–136
3	Du Z, Zhou B, Trinajstić N. Minimum sum-connectivity indices of trees and unicyclic graphs of a given matching number. J Math Chem, 2010, 47: 842–855 https://doi.org/10.1007/s10910-009-9604-7
4	Li X, Gutman I. Mathematical Aspects of Randić-type Molecular Structure Descriptors. Mathematical Chemistry Monographs, No 1. Kragujevac: University of Kragujevac 2006
5	Li X, Shi Y, A survey on the Randić index. MATCH Commun Math Comput Chem, 2008, 59(1): 127–156
6	Randić M. On characterization of molecular branching. J Am Chem Soc, 1975, 97: 6609–6615 https://doi.org/10.1021/ja00856a001
7	Tache R M. General sum-connectivity index with alpha>= 1 for bicyclic graphs. MATCH Commun Math Comput Chem, 2014, 72: 761–774
8	Todeschini R, Consonni V. Handbook of Molecular Descriptors. Weinheim: Wiley–VCH, 2000 https://doi.org/10.1002/9783527613106
9	Tomescu I, Jamil M K. Maximum general sum-connectivity index for trees with given independence number. MATCH Commun Math Comput Chem, 2014, 72: 715–722
10	Tomescu I, Kanwal S. Ordering trees having small general sum-connectivity index. MATCH Commun Math Comput Chem, 2013, 69: 535–548
11	Wang S, Zhou B, Trinajstic N. On the sum-connectivity index. Filomat, 2011, 25(3):29–42 https://doi.org/10.2298/FIL1103029W
12	Xing R, Zhou B, Trinajstic N. Sum-connectivity index of molecular trees. J Math Chem, 2010, 48: 583–591 https://doi.org/10.1007/s10910-010-9693-3
13	Zhou B, Trinajstić N. On a novel connectivity index. J Math Chem, 2009, 46: 1252–1270 https://doi.org/10.1007/s10910-008-9515-z

[1]	Wen-Huan WANG, Ling YUAN. Uniform supertrees with extremal spectral radii[J]. Front. Math. China, 2020, 15(6): 1211-1229.
[2]	Yizheng FAN, Zhu ZHU, Yi WANG. Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices[J]. Front. Math. China, 2020, 15(3): 451-465.
[3]	Hongmei YAO, Li MA, Chunmeng LIU, Changjiang BU. Brualdi-type inclusion sets of Z-eigenvalues and l^k,s-singular values for tensors[J]. Front. Math. China, 2020, 15(3): 601-612.
[4]	Xin LI, Jiming GUO, Zhiwen WANG. Minimal least eigenvalue of connected graphs of order n and size m = n + k (5≤k≤8)[J]. Front. Math. China, 2019, 14(6): 1213-1230.
[5]	Lihua YOU, Xiaohua HUANG, Xiying YUAN. Sharp bounds for spectral radius of nonnegative weakly irreducible tensors[J]. Front. Math. China, 2019, 14(5): 989-1015.
[6]	Kinkar Chandra DAS, Huiqiu LIN, Jiming GUO. Distance signless Laplacian eigenvalues of graphs[J]. Front. Math. China, 2019, 14(4): 693-713.
[7]	Thomas BRÜSTLE, Jie ZHANG. Non-leaving-face property for marked surfaces[J]. Front. Math. China, 2019, 14(3): 521-534.
[8]	Ziqiu LIU, Yunfeng ZHAO, Yuqin ZHANG. Perfect 3-colorings on 6-regular graphs of order 9[J]. Front. Math. China, 2019, 14(3): 605-618.
[9]	Jun HE, Yanmin LIU, Junkang TIAN, Xianghu LIU. Upper bounds for signless Laplacian Z-spectral radius of uniform hypergraphs[J]. Front. Math. China, 2019, 14(1): 17-24.
[10]	Xiaoxiao ZHANG, Aijin LIN. Positive solutions of p-th Yamabe type equations on graphs[J]. Front. Math. China, 2018, 13(6): 1501-1514.
[11]	Xiaofeng XUE. Phase transition for SIR model with random transition rates on complete graphs[J]. Front. Math. China, 2018, 13(3): 667-690.
[12]	Zhihe LIANG. *Super (a, d)-edge-antimagic total labelings of complete bipartite graphs*[J]. Front. Math. China, 2018, 13(1): 129-146.
[13]	Xiying YUAN, Xuelian SI, Li ZHANG. Ordering uniform supertrees by their spectral radii[J]. Front. Math. China, 2017, 12(6): 1393-1408.
[14]	Dongmei CHEN, Zhibing CHEN, Xiao-Dong ZHANG. Spectral radius of uniform hypergraphs and degree sequences[J]. Front. Math. China, 2017, 12(6): 1279-1288.
[15]	Shiying WANG, Zhenhua WANG, Mujiangshan WANG, Weiping HAN. *g-Good-neighbor conditional diagnosability of star graph networks under PMC model and MM model**[J]. Front. Math. China, 2017, 12(5): 1221-1234.

Viewed

Full text

Abstract

Cited

Shared

Discussed