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Full-Text Articles in Physical Sciences and Mathematics
The Minimum Span Of L(2,1)-Labelings Of Certain Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Matthew Tesch, Denise Troxell, Cody Wheeland
The Minimum Span Of L(2,1)-Labelings Of Certain Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Matthew Tesch, Denise Troxell, Cody Wheeland
Sarah Spence Adams
In the classical channel assignment problem, transmitters that are sufficiently close together are assigned transmission frequencies that differ by prescribed amounts, with the goal of minimizing the span of frequencies required. This problem can be modeled through the use of an L(2,1)-labeling, which is a function f from the vertex set of a graph G to the non-negative integers such that |f(x)–f(y)|≥ 2 if xand y are adjacent vertices and |f(x)–f(y)|≥1 if xand y are at distance two. The goal is to …
An Extension Of The Channel-Assignment Problem: L(2, 1)-Labelings Of Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Denise Troxell
An Extension Of The Channel-Assignment Problem: L(2, 1)-Labelings Of Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Denise Troxell
Sarah Spence Adams
The channel-assignment problem involves assigning frequencies represented by nonnegative integers to radio transmitters such that transmitters in close proximity receive frequencies that are sufficiently far apart to avoid interference. In one of its variations, the problem is commonly quantified as follows: transmitters separated bythe smallest unit distance must be assigned frequencies that are at least two apart and transmitters separated by twice the smallest unit distance must be assigned frequencies that are at least one apart. Naturally, thischannel-assignment problem can be modeled with vertex labelings of graphs. An L(2, 1)-labeling of a graph G is a function f from the …
On The Hole Index Of L(2,1)-Labelings Of R-Regular Graphs, Sarah Adams, Matthew Tesch, Denise Troxell, Bradford Westgate, Cody Wheeland
On The Hole Index Of L(2,1)-Labelings Of R-Regular Graphs, Sarah Adams, Matthew Tesch, Denise Troxell, Bradford Westgate, Cody Wheeland
Sarah Spence Adams
An L(2,1)-labeling of a graph G is an assignment of nonnegative integers to the vertices of G so that adjacent vertices get labels at least distance two apart and vertices at distance two get distinct labels. A hole is an unused integer within the range of integers used by the labeling. The lambda number of a graphG, denoted λ(G), is the minimum span taken over all L(2,1)-labelings of G. The hole index of a graph G, denoted ρ(G), is the minimum number of holes taken over all L(2,1)-labelings with span exactly λ(G). Georges and Mauro [On the structure of graphs …
Labeling Matched Sums With A Condition At Distance Two, Sarah Spence Adams, Denise Troxell
Labeling Matched Sums With A Condition At Distance Two, Sarah Spence Adams, Denise Troxell
Sarah Spence Adams
An L(2,1)-labeling of a graph G is a function f:V(G)→{0,1,…,k} such that |f(x)−f(y)|≥2 if x and y are adjacent vertices, and |f(x)−f(y)|≥1 if x and y are at distance 2. Such labelings were introduced as a way of modeling the assignment of frequencies to transmitters operating in close proximity within a communications network. The lambda number of G is the minimum k over all L(2,1)-labelings of G. This paper considers the lambda number of the matched sum of two same-order disjoint graphs, wherein the graphs have been connected by a perfect matching between the two vertex sets. Matched sums have …
Exact Lambda-Numbers Of Generalized Petersen Graphs Of Certain Higher-Orders And On Mobius Strips, Sarah Spence Adams, Paul Booth, Harold Jaffe, Denise Troxell, Luke Zinnen
Exact Lambda-Numbers Of Generalized Petersen Graphs Of Certain Higher-Orders And On Mobius Strips, Sarah Spence Adams, Paul Booth, Harold Jaffe, Denise Troxell, Luke Zinnen
Sarah Spence Adams
An L(2,1)-labeling of a graph G is an assignment f of nonnegative integers to the vertices of G such that if vertices x and y are adjacent, |f(x)−f(y)|≥2, and if x and y are at distance two, |f(x)−f(y)|≥1. The λ-number of Gis the minimum span over all L(2,1)-labelings of G. A generalized Petersen graph (GPG) of order n consists of two disjoint copies of cycles on n vertices together with a perfect matching between the two vertex sets. By …