具有较大Randić指数的仙人掌图

doi:10.15960/j.cnki.issn.1007-6093.2020.04.012

Abstract

Abstract: The Randić index was one of the most important molecular topological indices, and became a popular topic of research in mathematics and mathematical chemistry. The sharp upper and lower bounds of Randić index of trees, unicyclic graphs and bicyclic graphs have been obtained. Furthermore, the minimal graphs of trees, unicyclic graphs and bicyclic graphs on Randić index have been characterized. In addition, the lower bounds of cacti on Randić index and corresponding extremal graphs have been described. In this paper, we analyzed the degrees of vertices of the edges in cacti, defined the symmetric edges and the asymmetric edges, and characterized some transformations. Based on these definitions, we discussed in terms of maximum degree of vertices. In the end, the extremal graphs have been characterized by the asymmetric edges in cacti of n-vertex given the number of circles with the first, the second, the third, the fourth and the fifth maximum Randić index.

Key words: Randić index, cacti, asymmetric edge

CLC Number:

O157.5

WANG Yajing, GAO Yubin. Cacti with larger Randić index[J]. Operations Research Transactions, 2020, 24(4): 135-144.

[1]	LAN Yongxin, SHI Yongtang, SONG Zixia. Planar Turán number and planar anti-Ramsey number of graphs [J]. Operations Research Transactions, 2021, 25(3): 200-216.
[2]	TIAN Shuangliang, YANG Huan, SUOLANG Wangqing, YANG Qing. Neighbor sum distinguishing edge coloring of the lexicographic product of paths [J]. Operations Research Transactions, 2020, 24(1): 140-146.
[3]	TAO Yanliang, HUANG Qiongxiang, CHEN Lin. Contraction graph method for the interval edge-colorings of graphs [J]. Operations Research Transactions, 2019, 23(2): 31-43.
[4]	LIU Yan, LEI Mengxia, HUANG Xiaoxian. Path-transformation graph of maximum matchings [J]. Operations Research Transactions, 2019, 23(2): 104-112.
[5]	LUO Zhaoyang, SUN Lin. The linear aboricity of planar graphs with 6-cycles containing at most one chord [J]. Operations Research Transactions, 2019, 23(2): 113-119.
[6]	PEI Jianfeng, LIN Shangwei. Two sufficient conditions for maximally restricted-edge-connected hypergraphs [J]. Operations Research Transactions, 2019, 23(2): 120-126.
[7]	SUN Qiushi, YANG Xiaoyun, WANG Ligong, LI Xihe, WANG Pengchao. Laplacian spectral characterizations of new unicyclic graphs H(p,tK_1,m) [J]. Operations Research Transactions, 2019, 23(1): 72-80.
[8]	CHEN Yuanyuan, WANG Guoping. On the signless Laplacian spectral radius of tricyclic graphs [J]. Operations Research Transactions, 2019, 23(1): 81-89.
[9]	CHEN Hongyu, TAN Xiang. An upper bound of the linear 2-arboricity of planar graphs with neither 5-cycles nor adjacent 4-cycles [J]. Operations Research Transactions, 2019, 23(1): 104-110.
[10]	REN Jiamin, FENG Wei, ZHAO Lingqi, WANG Shiying, JIRIMUTU. The 1-good-neighbor diagnosability of the Cayley graphs UG_n generated by unicyclic graphs under the PMC model and the MM^* model [J]. Operations Research Transactions, 2019, 23(1): 97-103.
[11]	MEI Ruoxing, WANG Ligong, WANG Luhua, WANG Zhanqing. Laplacian spectral characterizations of unicyclic graphs H( p, t K_{ 1, m}) [J]. Operations Research Transactions, 2015, 19(1): 57-64.
[12]	HU Xiaochen, HE Weili, HAO Rongxia. Balanced judicious partitions of graphs with $\Delta($G$)-\delta($G$)\leq$2 [J]. Operations Research Transactions, 2015, 19(1): 108-116.
[13]	SUN Lin, LUO Zhaoyang. Edge colourings of embedded special graphs [J]. Operations Research Transactions, 2015, 19(1): 125-130.
[14]	SONG Sulin, LIN Limei, ZHOU Shuming. The t/k-diagnosability and diagnosis algorithm of Pancake networks [J]. Operations Research Transactions, 2014, 18(4): 65-77.
[15]	XIAO Mao, WANG Wenhuan. Minimal skew energies of oriented bicyclic graphs without even cycles [J]. Operations Research Transactions, 2014, 18(4): 85-95.

Cacti with larger Randić index

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments