منابع مشابه
Detour Monophonic Graphoidal Covering Number of Corona Product Graph of Some Standard Graphs with the Wheel
A chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path $P$ is called a monophonic path if it is a chordless path. A longest $x-y$ monophonic path is called an $x-y$ detour monophonic path. A detour monophonic graphoidal cover of a graph $G$ is a collection $psi_{dm}$ of detour monophonic paths in $G$ such that every vertex of $G$ is an internal vertex of at most on...
متن کاملOn the Equivalence Covering Number of Splitgraphs
An equivalence graph is a disjoint union of cliques. For a graph G let eq(G) be the minimum number of equivalence subgraphs of G needed to cover all edges of G. We call eq( G) the equivalence covering number of G. It was shown in [ 81 that computing the equivalence covering number is NP-hard, even when restricted to graphs in which no two triangles have a vertex in common. We show that the equi...
متن کاملThe covering number of M 24
A finite cover C of a group G is a finite collection of proper subgroups of G such that G is equal to the union of all of the members of C. Such a cover is called minimal if it has the smallest cardinality among all finite covers of G. The covering number of G, denoted by σ(G), is the number of subgroups in a minimal cover of G. In this paper the covering number of the Mathieu group M24 is show...
متن کاملThe chromatic covering number of a graph
Following [1], we investigate the problem of covering a graph G with induced subgraphs G1, . . . , Gk of possibly smaller chromatic number, but such that for every vertex u of G, the sum of reciproquals of the chromatic numbers of the Gi’s containing u is at least 1. The existence of such “chromatic coverings” provides some bounds on the chromatic number of G.
متن کاملOn the Fractional Covering Number of Hypergraphs
The fractional covering number r* of a hypergraph H (V, E) is defined to be the minimum possible value of ,, v t(x) where ranges over all functions t: V which satisfy ,xe t(x) >= for all edges e e E. In the case of ordinary graphs G, it is known that 2r*(G) is always an integer. By contrast, it is shown (among other things) that for any rational p/q >= 1, there is a 3-uniform hypergraph H with-...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.03.011