Correction to: Burning Numbers of t-unicyclic Graphs

The largest Wiener index of unicyclic graphs given girth or maximum degree

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-015-0971-x ◽

2015 ◽

Vol 53 (1-2) ◽

pp. 343-363 ◽

Cited By ~ 4

Author(s):

Shang-wang Tan ◽

Yan Lin

Keyword(s):

Maximum Degree ◽

Wiener Index ◽

Unicyclic Graphs

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On the Reverse Wiener Indices of Unicyclic Graphs

Acta Applicandae Mathematicae ◽

10.1007/s10440-008-9298-z ◽

2008 ◽

Vol 106 (2) ◽

pp. 293-306 ◽

Cited By ~ 5

Author(s):

Zhibin Du ◽

Bo Zhou

Keyword(s):

Unicyclic Graphs

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Hop Domination in Graphs-II

Analele Universitatii Ovidius Constanta - Seria Matematica ◽

10.1515/auom-2015-0036 ◽

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.

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

Asian-European Journal of Mathematics ◽

10.1142/s1793557122500693 ◽

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).

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