k-connectivity of uniform s-intersection graphs
نویسندگان
چکیده
منابع مشابه
K-connectivity of Uniform S-intersection Graphs
Let W1, . . . ,Wn be independent random subsets of [m] = {1, . . . ,m}. Assuming that each Wi is uniformly distributed in the class of d-subsets of [m] we study the uniform random intersection graph Gs(n,m, d) on the vertex set {W1, . . .Wn}, defined by the adjacency relation: Wi ∼ Wj whenever |Wi ∩Wj | ≥ s. We show that as n,m → ∞ the edge density threshold for the property that each vertex of...
متن کاملResults on Vertex Degree and K-Connectivity in Uniform S-Intersection Graphs (CMU-CyLab-14-004)
We present results related to the vertex degree in a uniform s-intersection graph which has received much interest recently. Specifically , we derive the probability distribution for the minimum vertex degree, and show that the number of vertices with an arbitrary degree converges to a Poisson distribution. A uniform s-intersection graph models the topology of a secure wireless sensor network e...
متن کاملResults on Vertex Degree and K-Connectivity in Uniform S-Intersection Graphs
Abstract. We present results related to the vertex degree in a uniform s-intersection graph which has received much interest recently. Specifically, we derive the probability distribution for the minimum vertex degree, and show that the number of vertices with an arbitrary degree converges to a Poisson distribution. A uniform s-intersection graph models the topology of a secure wireless sensor ...
متن کاملOn k-Connectivity and Minimum Vertex Degree in Random s-Intersection Graphs
Random s-intersection graphs have recently received much interest in a wide range of application areas. Broadly speaking, a random s-intersection graph is constructed by first assigning each vertex a set of items in some random manner, and then putting an undirected edge between all pairs of vertices that share at least s items (the graph is called a random intersection graph when s = 1). A spe...
متن کاملConnectivity of the uniform random intersection graph
A uniform random intersection graph G(n,m, k) is a random graph constructed as follows. Label each of n nodes by a randomly chosen set of k distinct colours taken from some finite set of possible colours of size m. Nodes are joined by an edge if and only if some colour appears in both their labels. These graphs arise in the study of the security of wireless sensor networks, in particular when m...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2014
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.06.014