نتایج جستجو برای: connectivity
تعداد نتایج: 65970 فیلتر نتایج به سال:
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We define a boundary defensive k-alliance in a graph as a set S of vertices with the property that every vertex in S has exactly k more neighbors in S than it has outside of S. In this paper we study mathematical properties of boundary defensive k-alliances. In particular, we obtain several bounds on the cardinality of every boundary defensive k-alliance. Moreover, we consider the case in which...
We consider a variant of the Cops and Robbers game where the robber can move s edges at a time, and show that in this variant, the cop number of a connected graph on n vertices can be as large as Ω(n s s+1 ). This improves the Ω(n s−3 s−2 ) lower bound of Frieze et al. [5], and extends the result of the second author [10], which establishes the above bound for s = 2, 4.
Goal In a contaminated network, an invisible omniscient arbitrary fast fugitive ; a team of searchers ; We want to find a strategy that catch the fugitive using the fewest searchers as possible. Goal In a contaminated network, an invisible omniscient arbitrary fast fugitive ; a team of searchers ; We want to find a strategy that catch the fugitive using the fewest searchers as possible.
A simple connected graph G is said to be interval distance monotone if the interval I (u, v) between any pair of vertices u and v in G induces a distance monotone graph. Aïder and Aouchiche [Distance monotonicity and a new characterization of hypercubes, Discrete Math. 245 (2002) 55–62] proposed the following conjecture: a graph G is interval distance monotone if and only if each of its interva...
Let G be a simple connected graph with n vertices and n edges which we call an unicyclic graph. In this paper, we first investigate the least eigenvalue λn(G), then we present two sharp bounds of the spread s(G) of G. AMS classification: 05C50 ,05C35
Let G be a connected graph. For a vertex v ∈ V (G) and an ordered k-partition Π = {S1, S2, ..., Sk} of V (G), the representation of v with respect to Π is the k-vector r(v|Π) = (d(v, S1), d(v, S2), ..., d(v, Sk)). The k-partition Π is said to be resolving if the k-vectors r(v|Π), v ∈ V (G), are distinct. The minimum k for which there is a resolving k-partition of V (G) is called the partition d...
As a measure of the extent to which the removal of a node disconnects a graph, the cutting number c(v) of a node v in a connected graph G has been defined to be the number of pairs of nodes in different components of G {v}. We present a linear algorithm for determining c(v) for all nodes of a tree, and hence for identifying the cutting center, which consists of the nodes v at which c(v) is maxi...
4 A 3-connected graph is 3-connected if it has no 3-separation that separates a “large” fan or K3,n 5 from the rest of the graph. It is proved in this paper that, except for K4, every 3 -connected graph has 6 a 3-connected proper minor that is at most two edges away from the original graph. This result is used 7 to characterize Q-minor-free graphs, where Q is obtained from the Cube by contracti...
The edge reconstruction number of a graph G, RN(G), is the minimum number of edge deleted subgraphs required to determine G up to isomorphism. We prove the following results for a disconnected graph G with at least two nontrivial components. If G has a pair of nontrivial nonisomorphic components then RN (G) ≤ 3. If G has a pair of nontrivial nonisomorphic components, is not a forest, and contai...
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