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.
| Identifer | oai:union.ndltd.org:csusb.edu/oai:scholarworks.lib.csusb.edu:etd-1132 |
| Date | 01 December 2014 |
| Creators | Alegria, Linda V |
| Publisher | CSUSB ScholarWorks |
| Source Sets | California State University San Bernardino |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses, Projects, and Dissertations |
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