Radio number for trees

Liu, Daphne Der-Fen

doi:10.1016/j.disc.2007.03.066

Cited by 76 publications

(24 citation statements)

References 12 publications

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“…Notice that when G is a tree, Proposition 2 gives a preliminary lower bound for the radio number of a tree. This is the same lower bound as given by Liu in Theorem 3 of [8] but with different notation. In Liu's proof, she shows that…”

Section: Lower Bound Techniquessupporting

confidence: 59%

“…This is a graph with no cycles. Work has been done to determine the radio numbers of various different types of tree graphs, including [7,8,9,10].…”

Section: Previous Results For Tree Graphsmentioning

confidence: 99%

“…In this thesis, we mostly look at particular types of tree graphs whose radio numbers are not yet known. In particular, we look at improving the lower bounds of the radio number for these tree graphs that was established in [8]. As we discuss in Chapter 3, in work with Maggy Tomova and Matthew Porter, we not only improve the lower bound, but find the radio number for all simple connected graphs with n vertices and diameter n − 2.…”

Section: Previous Results For Tree Graphsmentioning

confidence: 99%

“…As mentioned in Section 2.1, Liu establishes bounds for the radio numbers of trees in [8]. In particular she determines the exact radio numbers of spire graphs with an odd number of vertices and of spire graphs when the spire is very close to the middle of the path.…”

Section: Chapter 3 Graphs With N Vertices and Diameter N −mentioning

confidence: 99%

“…Work has been done to determine the radio number of various families of graphs. Some of the graphs whose radio numbers have been determined are paths, kpartite graphs, cycles, n-cubes, certain types of trees, certain types of spider graphs, m-ary trees, some thorn graphs, complete graphs, stars, wheels, gear graphs, and Cartesian products of complete graphs [3,4,6,7,8,9,10,11].…”

Section: Radio Labelingmentioning

confidence: 99%

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On Radio Labeling of Diameter N-2 and Caterpillar Graphs

Benson¹

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determined the radio number of complete m-ary trees [7]. Ruxandra Marinescu-Ghemeci found the radio number for some thorn graphs, one of which is a particular type of caterpillar graph [10]. This thesis builds off of work done on paths and trees in general to determine an improved lower bound or the actual radio number of certain types of caterpillar graphs. This thesis includes joint work with Matthew Porter and Maggy Tomova on determining the radio numbers of graphs with n vertices and diameter n − 2, a subcase of which is a particular caterpillar. This thesis also establishes the radio number of some specific caterpillar graphs as well as an improved lower bound for the radio number of more general caterpillar graphs. v TABLE OF CONTENTS LIST OF TABLES .

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Section: Lower Bound Techniquessupporting

confidence: 59%

“…This is a graph with no cycles. Work has been done to determine the radio numbers of various different types of tree graphs, including [7,8,9,10].…”

Section: Previous Results For Tree Graphsmentioning

confidence: 99%

Section: Previous Results For Tree Graphsmentioning

confidence: 99%

Section: Chapter 3 Graphs With N Vertices and Diameter N −mentioning

confidence: 99%

Section: Radio Labelingmentioning

confidence: 99%

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On Radio Labeling of Diameter N-2 and Caterpillar Graphs

Benson¹

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Distance edge coloring and collision‐free communication in wireless sensor networks

Drira¹,

Effantin²,

Kheddouci³

2013

Networks

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Motivated by the problem of link scheduling in wireless sensor networks where different sensors have different transmission and interference ranges and may be mobile, we study the problem of "distance edge coloring" of graphs, which is a generalization of proper edge coloring. Let G be a graph modeling a sensor network. An -distance edge coloring of G is a coloring of the edges of G such that any two edges within distance of each other are assigned different colors. The parameter is chosen, so that the links corresponding to two edges that are assigned the same color do not interfere. We investigate the -distance edge coloring problem on several families of graphs that can be used as topologies in sensor deployment. We focus on determining the minimum number of colors needed and optimal coloring algorithms.

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A Lower Bound for the Radio Number of Graphs

Bantva¹

2019

Algorithms and Discrete Applied Mathematics

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A radio labeling of a graph G is a mapping ϕ : u, v) for every pair of distinct vertices u, v of G, where diam(G) and d(u, v) are the diameter of G and distance between u and v in G, respectively. The radio number rn(G) of G is the smallest number k such that G has radio labeling with max{ϕ(v) : v ∈ V (G)} = k. In this paper, we slightly improve the lower bound for the radio number of graphs given by Das et al. in [5] and, give necessary and sufficient condition to achieve the lower bound. Using this result, we determine the radio number for cartesian product of paths Pn and the Peterson graph P . We give a short proof for the radio number of cartesian product of paths Pn and complete graphs Km given by Kim et al. in [6].

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Radio number for trees

Cited by 76 publications

References 12 publications

On Radio Labeling of Diameter N-2 and Caterpillar Graphs

On Radio Labeling of Diameter N-2 and Caterpillar Graphs

Distance edge coloring and collision‐free communication in wireless sensor networks

A Lower Bound for the Radio Number of Graphs

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