Displaying similar documents to “Constant 2-Labellings And An Application To (R, A, B)-Covering Codes”

Heavy cycles in weighted graphs

J. Adrian Bondy, Hajo J. Broersma, Jan van den Heuvel, Henk Jan Veldman (2002)

Discussiones Mathematicae Graph Theory

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An (edge-)weighted graph is a graph in which each edge e is assigned a nonnegative real number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges, and an optimal cycle is one of maximum weight. The weighted degree w(v) of a vertex v is the sum of the weights of the edges incident with v. The following weighted analogue (and generalization) of a well-known result by Dirac for unweighted graphs is due to Bondy and Fan. Let G be a 2-connected weighted...

A σ₃ type condition for heavy cycles in weighted graphs

Shenggui Zhang, Xueliang Li, Hajo Broersma (2001)

Discussiones Mathematicae Graph Theory

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A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree d w ( v ) of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted graph which satisfies the following conditions: 1. The weighted degree sum of any three independent vertices is at least m; 2. w(xz) = w(yz)...

An Implicit Weighted Degree Condition For Heavy Cycles

Junqing Cai, Hao Li, Wantao Ning (2014)

Discussiones Mathematicae Graph Theory

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For a vertex v in a weighted graph G, idw(v) denotes the implicit weighted degree of v. In this paper, we obtain the following result: Let G be a 2-connected weighted graph which satisfies the following conditions: (a) The implicit weighted degree sum of any three independent vertices is at least t; (b) w(xz) = w(yz) for every vertex z ∈ N(x) ∩ N(y) with xy /∈ E(G); (c) In every triangle T of G, either all edges of T have different weights or all edges of T have the same weight. Then...

Digraphs are 2-weight choosable.

Khatirinejad, Mahdad, Naserasr, Reza, Newman, Mike, Seamone, Ben, Stevens, Brett (2011)

The Electronic Journal of Combinatorics [electronic only]

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Statuses and branch-weights of weighted trees

Chiang Lin, Jen-Ling Shang (2009)

Czechoslovak Mathematical Journal

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In this paper we show that in a tree with vertex weights the vertices with the second smallest status and those with the second smallest branch-weight are the same.

5-Stars of Low Weight in Normal Plane Maps with Minimum Degree 5

Oleg V. Borodin, Anna O. Ivanova, Tommy R. Jensen (2014)

Discussiones Mathematicae Graph Theory

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It is known that there are normal plane maps M5 with minimum degree 5 such that the minimum degree-sum w(S5) of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an M5 has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then w(S5) ≤ 68. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free M5 with w(S5) = 48