Research Article
On the Near-Common Neighborhood Graph of a Graph
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 149 - Issue 6 |
| Published: Sep 2016 |
| Authors: Ahmad N. Al-Kenani, Anwar Alwardi, Omar A. Al-Attas |
10.5120/ijca2016911411
|
Ahmad N. Al-Kenani, Anwar Alwardi, Omar A. Al-Attas . On the Near-Common Neighborhood Graph of a Graph. International Journal of Computer Applications. 149, 6 (Sep 2016), 1-4. DOI=10.5120/ijca2016911411
@article{ 10.5120/ijca2016911411,
author = { Ahmad N. Al-Kenani,Anwar Alwardi,Omar A. Al-Attas },
title = { On the Near-Common Neighborhood Graph of a Graph },
journal = { International Journal of Computer Applications },
year = { 2016 },
volume = { 149 },
number = { 6 },
pages = { 1-4 },
doi = { 10.5120/ijca2016911411 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2016
%A Ahmad N. Al-Kenani
%A Anwar Alwardi
%A Omar A. Al-Attas
%T On the Near-Common Neighborhood Graph of a Graph%T
%J International Journal of Computer Applications
%V 149
%N 6
%P 1-4
%R 10.5120/ijca2016911411
%I Foundation of Computer Science (FCS), NY, USA
Abstract
The near common-neighborhood graph of a graph G, denoted by ncn(G), is the graph on the some vertices ofG, two vertices being adjacent in ncn(G) if there is at least one vertex in G not adjacent to both of them. A graph is called near-common neighborhood graph if it is the near-common neighborhood of some graph. In this paper we introduce the near-common neighborhood of a graph, the near common neighborhood graph, near-completeness number of a graph, basic properties of these new graphs are obtained and interesting results are established.
References
- A. N. Al-Kenani, A. Alwardi, O. A. Al-Attas, On the Non- Common Neighbourhood Energy of Graphs. Applied Mathematics, 6, (2015), 1183-1188
- A. Alwardi, N. D. Soner, Further results on the common neighbourhood domination and some related graphs, Advanced studies in contemporary mathematics, 24 (1) 2014), 19-32.
- A. Alwardi, N. D. Soner, I. Gutman, On the commonneighborhood energy of a graph, Bull. Acad. Serbe Sci. Arts (Cl. Sci. Math.) 143 (2011) 49-59.
- A. Alwardi, B. Arsic, I. Gutman, N. D. Soner, The common neighborhood graph and its energy, Iran. J. Math. Sci. Inf. 7(2) (2012) 1-8.
- A. S. Bonifcio, R. R. Rosa, I. Gutman, N. M. M. de Abreu, Complete common neighborhood graphs, Proceedings of Congreso LatinoIberoamericano de Investigacin Operativa , Simpsio Brasileiro de Pesquisa Operacional (2012) 4026-4032.
- F. Harary, Graph theory, Addison-Wesley, Reading Mass (1969).
- T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, Inc., New York (1998).
- Martin Knor, Borut Luzar, Riste Skrekovski and Ivan Gutman, OnWiener Index of Common Neighborhood Graphs, MATCH Commun. Math. Comput. Chem, 72(2014), 321-332.
- Samaneh Hossein-Zadeh, Ali Iranmanesh, Asma Hamzeh and Mohammad Ali Hosseinzadeh, On the common neighborhood graphs, Electronic Notes in Discrete Mathematics, 45(2014), 51-56.
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