pancyclic graphs
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2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Muhammad Javaid ◽  
Hafiz Usman Afzal ◽  
Ebenezer Bonyah

The idea of super a , 0 -edge-antimagic labeling of graphs had been introduced by Enomoto et al. in the late nineties. This article addresses super a , 0 -edge-antimagic labeling of a biparametric family of pancyclic graphs. We also present the aforesaid labeling on the disjoint union of graphs comprising upon copies of C 4 and different trees. Several problems shall also be addressed in this article.



Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Guidong Yu ◽  
Tao Yu ◽  
Xiangwei Xia ◽  
Huan Xu

A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n . In fact, it is NP-complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to be pancyclic in terms of the spectral radius and the signless Laplacian spectral radius of the graph.



2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Jia-Bao Liu ◽  
Hafiz Usman Afzal ◽  
Muhammad Javaid

Labeling of graphs with numbers is being explored nowadays due to its diverse range of applications in the fields of civil, software, electrical, and network engineering. For example, in network engineering, any systems interconnected in a network can be converted into a graph and specific numeric labels assigned to the converted graph under certain rules help us in the regulation of data traffic, connectivity, and bandwidth as well as in coding/decoding of signals. Especially, both antimagic and magic graphs serve as models for surveillance or security systems in urban planning. In 1998, Enomoto et al. introduced the notion of super a,0 edge-antimagic labeling of graphs. In this article, we shall compute super a,0 edge-antimagic labeling of the rooted product of Pn and the complete bipartite graph K2,m combined with the union of path, copies of paths, and the star. We shall also compute a super a,0 edge-antimagic labeling of rooted product of Pn with a special type of pancyclic graphs. The labeling provided here will also serve as super a′,2 edge-antimagic labeling of the aforesaid graphs. All the structures discussed in this article are planar. Moreover, our findings have also been illustrated with examples and summarized in the form of a table and 3D plots.



10.37236/9451 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Dennis Clemens ◽  
Pranshu Gupta ◽  
Fabian Hamann ◽  
Alexander Haupt ◽  
Mirjana Mikalački ◽  
...  

Waiter-Client games are played on some hypergraph $(X,\mathcal{F})$, where $\mathcal{F}$ denotes the family of winning sets. For some bias $b$, during each round of such a game Waiter offers to Client $b+1$ elements of $X$, of which Client claims one for himself while the rest go to Waiter. Proceeding like this Waiter wins the game if she forces Client to claim all the elements of any winning set from $\mathcal{F}$. In this paper we study fast strategies for several Waiter-Client games played on the edge set of the complete graph, i.e. $X=E(K_n)$, in which the winning sets are perfect matchings, Hamilton cycles, pancyclic graphs, fixed spanning trees or factors of a given graph.



2018 ◽  
Vol 34 (6) ◽  
pp. 1691-1711
Author(s):  
Megan Cream ◽  
Ronald J. Gould ◽  
Kazuhide Hirohata
Keyword(s):  


2018 ◽  
Vol 38 (3) ◽  
pp. 661
Author(s):  
Pavel Hrnčiar ◽  
Gabriela Monoszová
Keyword(s):  


Author(s):  
John C. George ◽  
Abdollah Khodkar ◽  
W. D. Wallis
Keyword(s):  


2015 ◽  
Vol 35 (2) ◽  
pp. 271
Author(s):  
Zhenming Bi ◽  
Ping Zhang
Keyword(s):  


2014 ◽  
Vol 31 (2) ◽  
pp. 912-917
Author(s):  
Emlee W. Nicholson ◽  
Bing Wei


2013 ◽  
Vol 161 (7-8) ◽  
pp. 1128-1136 ◽  
Author(s):  
Carol T. Zamfirescu
Keyword(s):  


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