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Distance in graphs
Fred Buckley,Frank Harary +1 more
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The article was published on 1990-01-01 and is currently open access. It has received 1185 citations till now. The article focuses on the topics: Graph theory & Convexity.read more
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An upper bound on Wiener Indices of maximal planar graphs
Zhongyuan Che,Karen L. Collins +1 more
TL;DR: This paper shows that the diameter of G is at most ⌊ 1 3 ( n + 1 ) ⌋ , and the status of a vertex of G are sharp bounds and can be realized by an Apollonian network, which is a chordal maximal planar graph.
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Steiner Distance in Product Networks
Yaping Mao,Eddie Cheng,Zhao Wang +2 more
TL;DR: In this paper, the Steiner distance and Steiner $k-diameter of Cartesian and lexicographical product graphs were investigated, and they were shown to be the minimum size among all connected subgraphs whose vertex sets contain at least 2 vertices.
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Directed distance in digraphs: centers and medians
TL;DR: It is shown that for every two asymmetricDigraphs D1 and D2, there exists a strong asymmetric digraph H such that C(H) ≅ D 1 and M(H%) ≅D2, and where the directed distance from C(h) to M( H) and from M( h) to C (H) can be arbitrarily prescribed.
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Objective measures for sentinel surveillance in network epidemiology.
TL;DR: A comparison of the susceptible-infectious-recovered model on static and temporal networks of human contacts shows that, for some regions of parameter space, the three objective measures can rank the nodes very differently, meaning sentinel surveillance is a class of problems, and solutions need to chose an objective measure for the particular scenario in question.
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Average eccentricity, k-packing and k-domination in graphs
TL;DR: Upper bounds on the average eccentricity of graphs in terms of order and either k -packing number, k -domination number or connected k -Domination number are presented.