Title: | SOME NEW RESULTS ON CHROMATIC TRANSVERSAL DOMINATION IN GRAPHS |
Authors: | Vaidya, S. K., Parmar, A. D |
Keywords: | Coloring Domination, Chromatic Transversal Dominating Set. |
Issue Date: | 2019 |
Publisher: | Malaya Journal of Matematik |
Citation: | Vaidya, S. K., & Parmar, A. D. (2019). On chromatic transversal domination in graphs. Malaya Journal of Matematik, 7(03), 419-422. |
Abstract: | A proper k - coloring of a graph G is a function f : V (G) → {1, 2, ..., k} such that f (u) 6 = f (v) for all uv ∈ E(G). The color class Si is the subset of vertices of G that is assigned to color i. The chromatic number χ(G) is the minimum number k for which G admits proper k - coloring. A color class in a vertex coloring of a graph G is a subset of V (G) containing all the vertices of the same color. The set D ⊆ V (G) of vertices in a graph G is called dominating set if every vertex v ∈ V (G) is either an element of D or is adjacent to an element of D. If C = {S1, S2, ..., Sk} is a k - coloring of a graph G then a subset D of V (G) is called a transversal of C if D ∩ Si 6 = φ for all i ∈ {1, 2, ..., k}. A dominating set D of a graph G is called a chromatic transversal dominating set (cdt - set) of G if D is transversal of every chromatic partition of G. Here we prove some characterizations and also investigate chromatic transversal domination number of some graphs. |
URI: | http://10.9.150.37:8080/dspace//handle/atmiyauni/1987 |
Appears in Collections: | 01. Journal Articles |
Files in This Item:
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SOME NEW RESULTS ON CHROMATIC TRANSVERSAL.pdf | 190.59 kB | Adobe PDF | View/Open |
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