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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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On a conjecture about the ratio of Wiener index in iterated line graphs
TL;DR: It is proved that among all trees on n vertices the path Pn has the smallest value of this ratio for k ≥ 3, and it is conjecture that the maximum value of the ratio is obtained for the complete graph.
Book ChapterDOI
Distances in Algebra
Michel Deza,Elena Deza +1 more
TL;DR: A group (G,⋅,e) is a set of elements with a binary operation called the group operation as discussed by the authors, which together satisfy the four fundamental properties of closure, associativity, identity, and inverse.
Journal ArticleDOI
On the status sequences of trees
TL;DR: In this paper, the status of a vertex v in a connected graph is the sum of the distances from v to all other vertices in the graph, and it is NP-complete to decide whether there exists a tree that has a given sequence of integers as its status sequence.
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A note on cycles in graphs with specified radius and diameter
TL;DR: In this article, it was shown that a graph of radius r and diameter d has a cycle of length at least 4 r-2d, i.e. for its circumference it holds 4 r −2d cycles.
Journal ArticleDOI
Certain Varieties of Resolving Sets of A Graph
TL;DR: In this article, the minimum cardinality of r-sets is computed for paths, cycles, complete graphs and wheels, in possible cases, particulary for paths and complete graphs.