منابع مشابه
Graphs vertex-partitionable into strong cliques
A graph is said to be well-covered if all its maximal independent sets are of the same size. In 1999, Yamashita and Kameda introduced a subclass of well-covered graphs, called localizable graphs and defined as graphs having a partition of the vertex set into strong cliques, where a clique in a graph is strong if it intersects all maximal independent sets. Yamashita and Kameda observed that all ...
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For any simple connected graph $G=(V,E)$, a defensive alliance is a subset $S$ of $V$ satisfying the condition that every vertex $vin S$ has at most one more neighbour in $V-S$ than it has in $S$. The minimum cardinality of any defensive alliance in $G$ is called the alliance number of $G$, denoted $a(G)$. In this paper, we introduce a new type of alliance number called $k$-strong alliance numb...
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1. Introduction. Let 0 < p < 1 be fixed and denote by G a random graph with point set N, the set of natural numbers, such that each edge occurs with probability p, independently of all other edges. In other words the random variables ei5 , 1 < i < j, defined by _ 1 if (i, j) is an edge of G, et '-0 if (i, j) is not an edge of G, are independent r .v.'s with P(e i, = 1) = p, P(eij = 0) = 1-p. De...
متن کاملDominating cliques in graphs
A set of vertices is a dominating set in a graph if every vertex not in the dominating set is adjacent to one or more vertices in the dominating set. A dominating clique is a dominating set that induces a complete subgraph. Forbidden subgraph conditions sufficient to imply the existence of a dominating clique are given. For certain classes of graphs, a polynomial algorithm is given for finding ...
متن کاملOn cliques in diameter graphs
Note that we assume of the sphere being embedded in R, and the unit distance included from the ambient space. Diameter graphs arise naturally in the context of Borsuk’s problem. In 1933 Borsuk [3] asked whether any set of diameter 1 in R can be partitioned into (d+1) parts of strictly smaller diameter. The positive answer to this question is called Borsuk’s conjecture. This was shown to be true...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2020
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22573