Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
421220 | Discrete Applied Mathematics | 2012 | 10 Pages |
Abstract
A kk-rainbow dominating function of a graph is a function ff from the vertices V(G)V(G) to 2[k]2[k] such that, for all v∈V(G)v∈V(G), either f(v)≠0̸f(v)≠0̸ or ⋃u∈N[v]f(u)={1,…,k}⋃u∈N[v]f(u)={1,…,k}. The kk-rainbow domatic number drk(G)drk(G) is the maximum integer dd such that there exists a set of kk-rainbow dominating functions f1,f2,…,fdf1,f2,…,fd with ∑i=1d|fi(v)|≤k for all v∈V(G)v∈V(G). We study thekk-rainbow domatic number by finding this number for some classes of graphs and improving upon some known general bounds.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Shinya Fujita, Michitaka Furuya, Colton Magnant,