scholarly journals The competition number of a graph and the dimension of its hole space

2012 ◽  
Vol 25 (3) ◽  
pp. 638-642 ◽  
Author(s):  
Suh-Ryung Kim ◽  
Jung Yeun Lee ◽  
Boram Park ◽  
Yoshio Sano
Keyword(s):  
Competition Number

Representation of competitions by complex neutrosophic information

2020 ◽  
Vol 39 (5) ◽  
pp. 7881-7897
Author(s):  
Saba Siddique ◽  
Uzma Ahmad ◽  
Wardat us Salam ◽  
Muhammad Akram ◽  
Florentin Smarandache
Keyword(s):  
Real Life ◽  
Minimal Graph ◽  
Research Article ◽  
Competition Graph ◽  
Proposed Model ◽  
Extended Approach ◽  
Generalized Complex ◽  
Neutrosophic Graph ◽  
Competition Number

The concept of generalized complex neutrosophic graph of type 1 is an extended approach of generalized neutrosophic graph of type 1. It is an effective model to handle inconsistent information of periodic nature. In this research article, we discuss certain notions, including isomorphism, competition graph, minimal graph and competition number corresponding to generalized complex neutrosophic graphs. Further, we describe these concepts by several examples and present some of their properties. Moreover, we analyze that a competition graph corresponding to a generalized complex neutrosophic graph can be represented by an adjacency matrix with suitable real life examples. Also, we enumerate the utility of generalized complex neutrosophic competition graphs for computing the strength of competition between the objects. Finally, we highlight the significance of our proposed model by comparative analysis with the already existing models.

scholarly journals On the double competition number

1998 ◽  
Vol 82 (1-3) ◽  
pp. 251-255 ◽  
Author(s):  
Zoltán Füredi
Keyword(s):  
Competition Number

Competition Numbers and Phylogeny Numbers of Connected Graphs and Hypergraphs

2020 ◽  
Vol 27 (01) ◽  
pp. 79-86
Author(s):  
Yanzhen Xiong ◽  
Soesoe Zaw ◽  
Yinfeng Zhu
Keyword(s):  
Connected Graph ◽  
Connected Graphs ◽  
Its Phylogeny ◽  
Competition Graph ◽  
Acyclic Digraph ◽  
Vertex Set ◽  
Competition Number

Let D be a digraph. The competition graph of D is the graph having the same vertex set with D and having an edge joining two different vertices if and only if they have at least one common out-neighbor in D. The phylogeny graph of D is the competition graph of the digraph constructed from D by adding loops at all vertices. The competition/phylogeny number of a graph is the least number of vertices to be added to make the graph a competition/phylogeny graph of an acyclic digraph. In this paper, we show that for any integer k there is a connected graph such that its phylogeny number minus its competition number is greater than k. We get similar results for hypergraphs.

scholarly journals The competition number of a generalized line graph is at most two

2012 ◽  
Vol Vol. 14 no. 2 (Graph Theory) ◽  
Author(s):  
Boram Park ◽  
Yoshio Sano
Keyword(s):  
Graph Theory ◽  
Necessary Conditions ◽  
Line Graph ◽  
Sufficient Conditions ◽  
Line Graphs ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
International Audience ◽  
Necessary And Sufficient ◽  
Competition Number

Graph Theory International audience In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one. In this paper, we generalize this result to the competition numbers of generalized line graphs, that is, we show that the competition number of a generalized line graph is at most two, and give necessary conditions and sufficient conditions for the competition number of a generalized line graph being one.

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