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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Radio Number for Fourth Power Paths

Alegria, Linda V 01 December 2014 (has links)
A path on n vertices, denoted by Pn, is a simple graph whose vertices can be ordered so that two vertices are adjacent if and only if they are consecutive in the order. A fourth power path, Pn4, is obtained from Pn by adding edges between any two vertices, u and v, whose distance in Pn, denoted by dPn(u,v), is less than or equal to four. The diameter of a graph G, denoted diam(G) is the greatest distance between any two distinct vertices of G. A radio labeling of a graph G is a function f that assigns to each vertex a label from the set {0,1,2,...} such that |f(u)−f(v)| ≥ diam(G)−d(u,v)+1 holds for any two distinct vertices, u and v in G (i.e., u, v ∈ V (G)). The greatest value assigned to a vertex by f is called the span of the radio labeling f, i.e., spanf =max{f(v) : v ∈ V (G)}. The radio number of G, rn(G), is the minimum span of f over all radio labelings f of G. In this paper, we provide a lower bound for the radio number of the fourth power path.

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