Proofs of the AutoGraphiX conjectures on the domination number, average eccentricity and proximity

2021 ◽  
Vol 289 ◽  
pp. 292-301
Author(s):  
Lidan Pei ◽  
Xiangfeng Pan ◽  
Kun Wang ◽  
Jing Tian
Keyword(s):  
Domination Number ◽  
Average Eccentricity

scholarly journals On autographix conjecture regarding domination number and average eccentricity

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 699-710 ◽  
Author(s):  
Li-Dan Pei ◽  
Xiang-Feng Pan ◽  
Jing Tian ◽  
Gui-Qin Peng
Keyword(s):  
Upper Bound ◽  
Dominating Set ◽  
Domination Number ◽  
Mean Value ◽  
Dominating Sets ◽  
Minimum Cardinality ◽  
Maximal Distance ◽  
The Mean ◽  
Average Eccentricity

The eccentricity of a vertex is the maximal distance from it to another vertex and the average eccentricity ecc(G) of a graph G is the mean value of eccentricities of all vertices of G. A set S ? V(G) is a dominating set of a graph G if NG(v) ? S ? 0 for any vertex v ? V(G)\S. The domination number (G) of G is the minimum cardinality of all dominating sets of G. In this paper, we correct an AutoGraphiX conjecture regarding the domination number and average eccentricity, and present a proof of the revised conjecture. In addition, we establish an upper bound on ?(T)-ecc(T) for an n-vertex tree T.

Medium Domination Number of Certain Graphs

2018 ◽  
Vol 6 (11) ◽  
pp. 130
Author(s):  
K. Uma Samundesvari ◽  
J. Maria Regila Baby
Keyword(s):  
Domination Number

In this paper the author have found out the medium domination number of Helm graph, Friendship graph.

Strong Domination Number of some Path Related Graphs

2017 ◽  
Vol 7 (1) ◽  
pp. 109
Author(s):  
S. K. Vaidya ◽  
Sejal Hiteshbhai Karkar
Keyword(s):  
Domination Number

On Disconnected Domination Number of a Graph

2013 ◽  
Vol 3 (2) ◽  
pp. 17
Author(s):  
S. Balamurugan ◽  
G. Prabakaran
Keyword(s):  
Domination Number

On the Variants of Domination Number of Certain Graphs

2019 ◽  
Vol 10 (4) ◽  
pp. 865-876
Author(s):  
S. Sarah Surya ◽  
Fathima Sana Afrin. S
Keyword(s):  
Domination Number
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