Realizable triples in dominator colorings
View/Open
Author
Fletcher, Douglas M.
Date
200706Advisor
Gera, Ralucca
Rasmussen, Craig
Metadata
Show full item recordAbstract
Given a graph G and its vertex set V(G), the chromatic number, Chi(G), represents the minimum number of colors required to color the vertices of G so that no two adjacent vertices have the same color. The domination number of G, gamma(G), the minimum number of vertices in a set S, where every vertex in the set ( ) V G S is adjacent to a vertex in S. The dominator chromatic number of the graph, Chi subd (G) represents the smallest number of colors required in a proper coloring of G with the additional property that every vertex dominates a color class. The ordered triple, (a, b, c), is realizable if a connected graph G exists with gamma(G) = a, Chi(G) = b, and Chi subd (G) = c. For every ordered triple, (a, b, c) of positive integers, if either (a) a=1 and b=c greater or equal 2 or (b) 2 less than or equal a, b less than c and c less than or equal to a + b, , previous work has shown that the triple is realizable. The bounds do not consider the case . In an effort to realize all the ordered triples, we explore graphs and graph classes with a = b = c = k greater than or equal to 2.
Collections
Related items
Showing items related by title, author, creator and subject.

Competitive Weighted Matching in Transversal Matroids
Dimitrov, N. B.; Plaxton, C.G. (201009);Consider a bipartite graph with a set of leftvertices and a set of rightvertices. All the edges adjacent to the same leftvertex have the same weight. We present an algorithm that, given the set of rightvertices and the ... 
Stratified domination in oriented graphs
Gera, Ralucca; Ping, Zhang (2007);An oriented graph is 2stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let H be a 2stratified oriented graph ... 
On stratification and domination in graphs
Gera, Ralucca; Ping, Zhang (2006);A graph G is 2stratified if its vertex set is partitioned into two classes (each of which is a stratum or a color class), where the vertices in one class are colored red and those in the other class are colored blue. Let ...