CERTAIN OPERATION OF GENERALIZED PETERSEN GRAPHS HAVING LOCATING-CHROMATIC NUMBER FIVE

2020 ◽  
Vol 24 (2) ◽  
pp. 83-97
Author(s):  
Agus Irawan ◽  
Asmiati ◽  
S. Suharsono ◽  
Kurnia Muludi ◽  
La Zakaria
Keyword(s):  
Chromatic Number ◽  
Generalized Petersen Graphs ◽  
Petersen Graphs

scholarly journals Game Chromatic Number of Generalized Petersen Graphs and Jahangir Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Ramy Shaheen ◽  
Ziad Kanaya ◽  
Khaled Alshehada
Keyword(s):  
Chromatic Number ◽  
Proper Coloring ◽  
Game Chromatic Number ◽  
Generalized Petersen Graphs ◽  
Minimum Number ◽  
Petersen Graphs ◽  
Jahangir Graph ◽  
Prism Graph

Let G = V , E be a graph, and two players Alice and Bob alternate turns coloring the vertices of the graph G a proper coloring where no two adjacent vertices are signed with the same color. Alice's goal is to color the set of vertices using the minimum number of colors, which is called game chromatic number and is denoted by χ g G , while Bob's goal is to prevent Alice's goal. In this paper, we investigate the game chromatic number χ g G of Generalized Petersen Graphs G P n , k for k ≥ 3 and arbitrary n , n -Crossed Prism Graph, and Jahangir Graph J n , m .

scholarly journals Double Roman Graphs in P(3k, k)

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 336
Author(s):  
Zehui Shao ◽  
Rija Erveš ◽  
Huiqin Jiang ◽  
Aljoša Peperko ◽  
Pu Wu ◽  
...  
Keyword(s):  
Minimum Weight ◽  
Domination Number ◽  
Roman Domination ◽  
Generalized Petersen Graphs ◽  
Roman Domination Number ◽  
Double Roman Domination ◽  
Petersen Graphs ◽  
Roman Dominating Function ◽  
Sharp Lower Bound ◽  
Dominating Function

A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3} with the properties that if f(u)=0, then vertex u is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and if f(u)=1, then vertex u is adjacent to at least one vertex assigned 2 or 3. The weight of f equals w(f)=∑v∈Vf(v). The double Roman domination number γdR(G) of a graph G is the minimum weight of a double Roman dominating function of G. A graph is said to be double Roman if γdR(G)=3γ(G), where γ(G) is the domination number of G. We obtain the sharp lower bound of the double Roman domination number of generalized Petersen graphs P(3k,k), and we construct solutions providing the upper bounds, which gives exact values of the double Roman domination number for all generalized Petersen graphs P(3k,k). This implies that P(3k,k) is a double Roman graph if and only if either k≡0 (mod 3) or k∈{1,4}.

scholarly journals On the 2-extendability of the generalized Petersen graphs

1989 ◽  
Vol 78 (1-2) ◽  
pp. 169-177 ◽  
Author(s):  
Gerald Schrag ◽  
Larry Cammack
Keyword(s):  
Generalized Petersen Graphs ◽  
Petersen Graphs

scholarly journals Exact λ-numbers of generalized Petersen graphs of certain higher-orders and on Möbius strips

2012 ◽  
Vol 160 (4-5) ◽  
pp. 436-447 ◽  
Author(s):  
Sarah Spence Adams ◽  
Paul Booth ◽  
Harold Jaffe ◽  
Denise Sakai Troxell ◽  
S. Luke Zinnen
Keyword(s):  
Generalized Petersen Graphs ◽  
Petersen Graphs

scholarly journals Generalizing the generalized Petersen graphs

2007 ◽  
Vol 307 (3-5) ◽  
pp. 534-543 ◽  
Author(s):  
Marko Lovrečič Saražin ◽  
Walter Pacco ◽  
Andrea Previtali
Keyword(s):  
Generalized Petersen Graphs ◽  
Petersen Graphs

On 2-rainbow domination in generalized Petersen graphs

2017 ◽  
Vol 2 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Kuo-Hua Wu ◽  
Yue-Li Wang ◽  
Chiun-Chieh Hsu ◽  
Chao-Cheng Shih
Keyword(s):  
Generalized Petersen Graphs ◽  
Rainbow Domination ◽  
Petersen Graphs
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