scholarly journals The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shengzhang Ren
Keyword(s):  
Domination Number ◽  
Fibonacci Cube ◽  
Lucas Cube

LetΓnandΛnbe then-dimensional Fibonacci cube and Lucas cube, respectively. Denote byΓ[un,k,z]the subgraph ofΓninduced by the end-vertexun,k,zthat has no up-neighbor. In this paper, the number of end-vertices and domination numberγofΓnandΛnare studied. The formula of calculating the number of end-vertices is given and it is proved thatγ(Γ[un,k,z])≤2k-1+1. Using these results, the larger bound on the domination numberγofΓnandΛnis determined.

scholarly journals Connectivity of Fibonacci cubes, Lucas cubes and generalized cubes

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Jernej Azarija ◽  
Sandi Klavžar ◽  
Jaehun Lee ◽  
Yoomi Rho
Keyword(s):  
Graph Theory ◽  
Positive Integer ◽  
Minimum Degree ◽  
Edge Connectivity ◽  
Binary Word ◽  
Fibonacci Cube ◽  
International Audience ◽  
Lucas Cube

Graph Theory International audience If f is a binary word and d a positive integer, then the generalized Fibonacci cube Qd(f) is the graph obtained from the d-cube Qd by removing all the vertices that contain f as a factor, while the generalized Lucas cube Qd(lucas(f)) is the graph obtained from Qd by removing all the vertices that have a circulation containing f as a factor. The Fibonacci cube Γd and the Lucas cube Λd are the graphs Qd(11) and Qd(lucas(11)), respectively. It is proved that the connectivity and the edge-connectivity of Γd as well as of Λd are equal to ⌊ d+2 / 3⌋. Connected generalized Lucas cubes are characterized and generalized Fibonacci cubes are proved to be 2-connected. It is asked whether the connectivity equals minimum degree also for all generalized Fibonacci/Lucas cubes. It was checked by computer that the answer is positive for all f and all d≤9.

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

INVERSE CLIQUE REGULAR DOMINATION NUMBER IN FUZZY GRAPHS

2020 ◽  
Vol 9 (5) ◽  
pp. 2895-2902
Author(s):  
S. Basheer Ahamed ◽  
M. Mohamed Riyazdeen ◽  
M. Magudeskumar
Keyword(s):  
Domination Number ◽  
Fuzzy Graphs
Sign in / Sign up

Export Citation Format

Share Document