منابع مشابه
Nordhaus-Gaddum type results for the Harary index of graphs
The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ ...
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1 Dipartimento di Informatica e Comunicazione Università degli Studi di Milano Via Comelico 39, 20135 Milano, Italy [email protected] 2 Dipartimento di Scienze dell’Informazione, Università di Bologna Mura A. Zamboni 7, 40127 Bologna, Italy [email protected] 3 Department of Computer Science, University of Verona strada Le Grazie, 15, 37134 Verona, Italy [email protected] 4 Faculty of Infor...
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Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.
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A graph G is said to be H(n,∆)-universal if it contains every graph on at most n vertices with maximum degree at most ∆. It is known that for any ε > 0 and any natural number ∆ there exists c > 0 such that the random graph G(n, p) is asymptotically almost surely H((1− ε)n,∆)universal for p ≥ c(log n/n). Bypassing this natural boundary, we show that for ∆ ≥ 3 the same conclusion holds when p n− ...
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The clustering of a graph is defined as the fraction of existing edges between the neighbors of a vertex and the maximum number of edges that could possibly exist among the neighbors, averaged over all the vertices of the graph. Unlike other important graph parameters the clustering is a local measure. A small-world graph is a graph which has a relatively low diameter (with respect to a regular...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2010
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm210-3-3