scholarly journals Erratum: Liu, W.; Ban, J.; Feng, L.; Cheng, T.; Emmert-Streib, F.; Dehmer, M. The Maximum Hosoya Index of Unicyclic Graphs with Diameter at Most Four. Symmetry 2019, 11, 1034

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1496
Author(s):  
Weijun Liu ◽  
Jingwen Ban ◽  
Lihua Feng ◽  
Tao Cheng ◽  
Frank Emmert-Streib ◽  
...  
Keyword(s):  
Hosoya Index ◽  
Unicyclic Graphs

The authors wish to make the following corrections to their paper [...]

scholarly journals The Maximum Hosoya Index of Unicyclic Graphs with Diameter at Most Four

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1034 ◽  
Author(s):  
Weijun Liu ◽  
Jingwen Ban ◽  
Lihua Feng ◽  
Tao Cheng ◽  
Frank Emmert-Streib ◽  
...  
Keyword(s):  
Small Diameter ◽  
Hosoya Index ◽  
Unicyclic Graphs

The Hosoya index of a graph is defined by the total number of the matchings of the graph. In this paper, we determine the maximum Hosoya index of unicyclic graphs with n vertices and diameter 3 or 4. Our results somewhat answer a question proposed by Wagner and Gutman in 2010 for unicyclic graphs with small diameter.

scholarly journals The largest n - 1 Hosoya indices of unicyclic graphs

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2573-2581 ◽  
Author(s):  
Guihai Yu ◽  
Lihua Feng ◽  
Aleksandar Ilic
Keyword(s):  
Independent Sets ◽  
Hosoya Index ◽  
Unicyclic Graphs ◽  
Molecular Graphs ◽  
Appl Math

The Hosoya index Z(G) of a graph G is defined as the total number of edge independent sets of G. In this paper, we extend the research of [J. Ou, On extremal unicyclic molecular graphs with maximal Hosoya index, Discrete Appl. Math. 157 (2009) 391-397.] and [Y. Ye, X. Pan, H. Liu, Ordering unicyclic graphs with respect to Hosoya indices and Merrifield-Simmons indices, MATCH Commun. Math. Comput. Chem. 59 (2008) 191-202.] and order the largest n - 1 unicyclic graphs with respect to the Hosoya index.

On the Reverse Wiener Indices of Unicyclic Graphs

2008 ◽  
Vol 106 (2) ◽  
pp. 293-306 ◽  
Author(s):  
Zhibin Du ◽  
Bo Zhou
Keyword(s):  
Unicyclic Graphs

scholarly journals Hop Domination in Graphs-II

2015 ◽  
Vol 23 (2) ◽  
pp. 187-199
Author(s):  
C. Natarajan ◽  
S.K. Ayyaswamy
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Total Domination ◽  
Minimum Cardinality ◽  
Unicyclic Graphs ◽  
The Family ◽  
Independent Domination ◽  
Domination In Graphs ◽  
Domination Numbers

Abstract Let G = (V;E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V - S, there exists u ∈ S such that d(u; v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γh(G). In this paper we characterize the family of trees and unicyclic graphs for which γh(G) = γt(G) and γh(G) = γc(G) where γt(G) and γc(G) are the total domination and connected domination numbers of G respectively. We then present the strong equality of hop domination and hop independent domination numbers for trees. Hop domination numbers of shadow graph and mycielskian graph of graph are also discussed.

Maximum total irregularity index of some families of graph with maximum degree n − 1

2021 ◽  
pp. 2250069
Author(s):  
Shamaila Yousaf ◽  
Akhlaq Ahmad Bhatti
Keyword(s):  
Maximum Degree ◽  
Discrete Math ◽  
Simple Approach ◽  
Unicyclic Graphs ◽  
Irregularity Index ◽  
Degree Of A Vertex ◽  
Tricyclic Graphs ◽  
Bicyclic Graphs ◽  
Appl Math

The total irregularity index of a graph [Formula: see text] is defined by Abdo et al. [H. Abdo, S. Brandt and D. Dimitrov, The total irregularity of a graph, Discrete Math. Theor. Comput. Sci. 16 (2014) 201–206] as [Formula: see text], where [Formula: see text] denotes the degree of a vertex [Formula: see text]. In 2014, You et al. [L. H. You, J. S. Yang and Z. F. You, The maximal total irregularity of unicyclic graphs, Ars Comb. 114 (2014) 153–160.] characterized the graph having maximum [Formula: see text] value among all elements of the class [Formula: see text] (Unicyclic graphs) and Zhou et al. [L. H. You, J. S. Yang, Y. X. Zhu and Z. F. You, The maximal total irregularity of bicyclic graphs, J. Appl. Math. 2014 (2014) 785084, http://dx.doi.org/10.1155/2014/785084 ] characterized the graph having maximum [Formula: see text] value among all elements of the class [Formula: see text] (Bicyclic graphs). In this paper, we characterize the aforementioned graphs with an alternative but comparatively simple approach. Also, we characterized the graphs having maximum [Formula: see text] value among the classes [Formula: see text] (Tricyclic graphs), [Formula: see text] (Tetracyclic graphs), [Formula: see text] (Pentacyclic graphs) and [Formula: see text] (Hexacyclic graphs).

scholarly journals A connection between the Kekulé structures of pentagonal chains and the Hosoya index of caterpillar trees

2017 ◽  
Vol 232 ◽  
pp. 230-234 ◽  
Author(s):  
Chuanqi Xiao ◽  
Haiyan Chen ◽  
Andrei M. Raigorodskii
Keyword(s):  
Hosoya Index ◽  
Kekulé Structures
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