scholarly journals Hamilton-Connected Mycielski Graphs∗

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Yuanyuan Shen ◽  
Xinhui An ◽  
Baonyindureng Wu
Keyword(s):  
Generalized Petersen Graphs ◽  
Petersen Graphs ◽  
Hamilton Connected

Jarnicki, Myrvold, Saltzman, and Wagon conjectured that if G is Hamilton-connected and not K 2 , then its Mycielski graph μ G is Hamilton-connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs G with δ G > V G / 2 , generalized Petersen graphs G P n , 2 and G P n , 3 , and the cubes G 3 . In addition, if G is pancyclic, then μ G is pancyclic.

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

[1,2]-Domination in generalized Petersen graphs

2015 ◽  
Vol 9 ◽  
pp. 3187-3191
Author(s):  
Chengye Zhao ◽  
Chao Zhang
Keyword(s):  
Generalized Petersen Graphs ◽  
Petersen Graphs

scholarly journals On the cop number of generalized Petersen graphs

2017 ◽  
Vol 340 (6) ◽  
pp. 1381-1388 ◽  
Author(s):  
Taylor Ball ◽  
Robert W. Bell ◽  
Jonathan Guzman ◽  
Madeleine Hanson-Colvin ◽  
Nikolas Schonsheck
Keyword(s):  
Generalized Petersen Graphs ◽  
Petersen Graphs
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