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Stratified Claw Domination in Prisms

Gary Chartrand1, Teresa W. Haynes2, Michael A. Henning3, Ping Zhang4
1 Department of Mathematics and Statistics Western Michigan University Kalamazoo, MI 49008 USA
2Department of Mathematics East Tennessee State University Johnson City, TN 37614-0002 USA
3Department of Mathematics University of Natal, Private Bag X01 Pietermaritzburg, 3209 South Africa
4Department of Mathematics and Statistics Western Michigan University Kalamazoo, MI 49008 USA

Abstract

A graph G is 2-stratified 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 F be a 2-stratified graph rooted at some blue vertex v. An F-coloring of a graph is a red-blue coloring of the vertices of G in which every blue vertex v belongs to a copy of F rooted at v. The F-domination number γF(G) is the minimum number of red vertices in an F-coloring of G. In this paper, we determine the F-domination number of the prisms Cn×K2 for all 2-stratified claws F rooted at a blue vertex.