On minimal energy of bipartite unicyclic graphs of a given bipartition

被引:0
|
作者
Wang, Dongdong
Hua, Hongbo [1 ]
机构
[1] Huaiyin Inst Technol, Dept Comp Sci, Huaian 223000, Jiangsu, Peoples R China
关键词
Bipartite unicyclic graph; Energy of graph; Spectrum of graph; Bipartition; TREES;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The energy of a graph G, denoted by E(G), is defined to be the sum of absolute values of all eigenvalues of the adjacency matrix of G. Let B(p, q) denote the set of bipartite unicyclic graphs with a (p, q)-bipartition, where q >= p >= 2. Recently, Li and Zhou [MATCH Commun. Math. Comput. Chem. 54 (2005) 379-388.] conjectured that for q >= 3, E (B (3, q)) > E (H (3, q)), where B(3, q) and H(3, q) are respectively graphs as shown in Fig.1. In this note, we show that this conjecture is true for 3 <= q <= 217. As a byproduct, we determined the graph with minimal energy among all graphs in B(3, q).
引用
收藏
页码:169 / 176
页数:8
相关论文
共 50 条
  • [31] On the Revised Szeged Index of Unicyclic Graphs with Given Diameter
    Yu, Aimei
    Peng, Kun
    Hao, Rong-Xia
    Fu, Jiahao
    Wang, Yingsheng
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (01) : 651 - 672
  • [32] The number of independent sets in unicyclic graphs with a given diameter
    Li, Shuchao
    Zhu, Zhongxun
    DISCRETE APPLIED MATHEMATICS, 2009, 157 (07) : 1387 - 1395
  • [33] On the maximal augmented Zagreb index of unicyclic graphs with given girth
    Li, Yibo
    Zhang, Ruiting
    Fan, Qiong
    DISCRETE APPLIED MATHEMATICS, 2024, 356 : 238 - 246
  • [34] THE HARMONIC INDEX FOR UNICYCLIC AND BICYCLIC GRAPHS WITH GIVEN MATCHING NUMBER
    Zhong, Lingping
    MISKOLC MATHEMATICAL NOTES, 2015, 16 (01) : 587 - 605
  • [35] Inertia and distance energy of line graphs of unicyclic graphs
    Zhang, Xiaoling
    DISCRETE APPLIED MATHEMATICS, 2019, 254 : 222 - 233
  • [36] Extremal problems on Sombor indices of unicyclic graphs with a given diameter
    Liu, Hechao
    COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (04):
  • [37] The number of independent sets of unicyclic graphs with given matching number
    Chen, Gong
    Zhu, Zhongxun
    DISCRETE APPLIED MATHEMATICS, 2012, 160 (1-2) : 108 - 115
  • [38] On the connective eccentricity index of trees and unicyclic graphs with given diameter
    Yu, Guihai
    Qu, Hui
    Tang, Lang
    Feng, Lihua
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 420 (02) : 1776 - 1786
  • [39] Maximum Laplacian energy of unicyclic graphs
    Das, Kinkar Ch.
    Fritscher, Eliseu
    Pinheiro, Lucelia Kowalski
    Trevisan, Vilmar
    DISCRETE APPLIED MATHEMATICS, 2017, 218 : 71 - 81
  • [40] MAXIMAL HARARY INDEX OF UNICYCLIC GRAPHS WITH A GIVEN MATCHING NUMBER
    Xu, Kexiang
    Das, Kinkar Ch.
    Hua, Hongbo
    Diudea, Mircea V.
    STUDIA UNIVERSITATIS BABES-BOLYAI CHEMIA, 2013, 58 (02): : 71 - 86