Optimal maximal graphs
Publish place: Transactions on Combinatorics، Vol: 11، Issue: 2
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_COMB-11-2_003
تاریخ نمایه سازی: 17 آبان 1400
Abstract:
An optimal labeling of a graph with n vertices and m edges is an injective assignment of the first n nonnegative integers to the vertices, that induces, for each edge, a weight given by the sum of the labels of its end-vertices with the property that the set of all induced weights consists of the first m positive integers. We explore the connection of this labeling with other well-known functions such as super edge-magic and \alpha-labelings. A graph with n vertices is maximal when the number of edges is ۲n-۳; all the results included in this work are about maximal graphs. We determine the number of optimally labeled graphs using the adjacency matrix. Several techniques to construct maximal graphs that admit an optimal labeling are introduced as well as a family of outerplanar graphs that can be labeled in this form.
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Authors
Christian Barrientos
Department of Mathematics, Valencia College, Orlando, FL ۳۲۸۳۲, U. S. A.
Maged Youssef
Department of Mathematics & Statistics, College of Sciences, Imam Mohammad Ibn Saud Islamic University, Riyadh ۱۱۶۲۳, Saudi Arabia