Rank Numbers for Graphs with Paths and Cycles
by McClive, Jacqueline N., M.S., ROCHESTER INSTITUTE OF TECHNOLOGY, 2011, 31 pages; 1490560

Abstract:

A coloring of a graph, G, is an assignment of positive integers to the vertices of the graph with one number assigned to each vertex, so that adjacent vertices are assigned different numbers. A k-ranking of a graph is a coloring that uses {1, 2, ..., k} with the requirement that every path between any two vertices labeled with the same number contains a vertex with a higher label. The rank number of a graph, denoted χr(G), is the smallest k such that G has a k-ranking. In this paper we seek rank numbers for four specific families of graphs. Each of these families of graphs contains at least one cycle as a subgraph.
 
AdviserDarren Narayan
SchoolROCHESTER INSTITUTE OF TECHNOLOGY
SourceMAI/ 49-05, p. , Apr 2011
Source TypeThesis
SubjectsMathematics
Publication Number1490560
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