The competition numbers of ternary Hamming graphs
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چکیده
منابع مشابه
The competition numbers of ternary Hamming graphs
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest numbe...
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The competition graph of a digraphD is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v inD such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number ...
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The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to...
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For a graph G, it is known to be a hard problem to compute the competition number k(G) of the graph G in general. In this paper, we give an explicit formula for the competition numbers of complete tripartite graphs.
متن کاملComplete Tripartite Graphs and their Competition Numbers
We present a piecewise formula for the competition numbers of the complete tripartite graphs. For positive integers x, y and z where 2 ≤ x ≤ y ≤ z, the competition number of the complete tripartite graph Kx,y,z is yz − z − y − x + 3 whenever x 6= y and yz − 2y − z + 4 otherwise.
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2011
ISSN: 0893-9659
DOI: 10.1016/j.aml.2011.04.012