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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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The geodetic numbers of graphs and digraphs
TL;DR: In this paper, a sufficient and necessary condition for the equality of g(G), g−(G) and g+(G) for connected graphs G is presented, which improves a result of Chartrand, Harary and Zhang.
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Ordering Unicyclic Graphs with Large Average Eccentricities
Yunfang Tang,Bo Zhou +1 more
TL;DR: In this paper, the eccentricity of a vertex u in a connected graph G is defined as the maximum distance from u to other vertices of G. The n-vertex unicyclic graphs with the i-th largest average eccentricity are determined for all i up to ⌊ n 2 ⌋ 1 with n � 6.
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On a conjecture about Wiener index in iterated line graphs of trees
TL;DR: This paper proves that there exists no nontrivial tree T and i>=3, such that W(L^i(T))=W(T), and proves this conjecture for trees which are not homeomorphic to the claw K"1","3 and H.
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On Relation Between Kirchhoff Index, Laplacian-Energy-Like Invariant and Laplacian Energy of Graphs
Kinkar Ch. Das,Kexiang Xu +1 more
TL;DR: In this article, an upper bound on Kf of graphs is presented, and relations between Kf, LEL and first Zagreb index of G are obtained for simple graphs of order n with m edges.
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Products of distance degree regular and distance degree injective graphs
TL;DR: In this paper, the authors considered Cartesian and normal products of DDR and DDI graphs, and some structural results have been obtained along with some characterizations, where the eccentricity of a vertex u is the maximum distance of u to any other vertex in G.