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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 Connected Detour Numbers of Special Classes of Connected Graphs
Ahmed Ali,Ali A. Ali +1 more
TL;DR: In this article, the authors considered finite finite connected graphs and defined the connected detour number as a subset of a graph such that the induced subgraph is connected and every vertex of the graph is connected.
Secondary and Internal Distances of Sets in Graphs
TL;DR: For any given type of a set of vertices in a connected graph G =(V,E), the smallest integer x,y : z such that all minimal (or maximal) sets S of the given type, where |V | > |S |≥ 2, have the property that every vertex v ∈ V − S is within distance at most x to a second vertex w ∈ S (shortest distance) and within distance y to another vertex w − S (second shortest distance) as mentioned in this paper.
Journal ArticleDOI
On eccentricity sequences of connected graphs
TL;DR: In this article, the authors survey the literature on the eccentricity sequence of a connected graph and make the following contribution: "The list of eccentricities of a graph G is the list of its eccentricities in non-increasing order".
On the nullity number of graphs
Mustapha Aouchiche,Pierre Hansen +1 more
TL;DR: Borders on the nullity of graphs are proved using the number of pendant neighbors in a graph and one of those bounds is an improvement of a known bound involving the domination number.
Ordering Trees with Perfect Matchings by Their Wiener Indices
TL;DR: In this article, the authors considered the Wiener index of trees with perfect matchings and characterized the eight trees with smallest Wiener indices among all trees of order 2( 11) mm t with perfect matching.