ON GRAPHS WITH EQUAL CHROMATIC TRANSVERSAL DOMINATION AND CONNECTED DOMINATION NUMBERS
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let G = (V, E) be a graph with chromatic number ${\chi}(G)$. dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every χ-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by ${\gamma}_{ct}$(G). In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number.
Abstract
Let G = (V, E) be a graph with chromatic number ${\chi}(G)$. dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every χ-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by ${\gamma}_{ct}$(G). In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number.
참고문헌 (8)
- S. Arumugam, "On graphs with equal domination and connected domi- nation numbers", Discrete Math, 206(1-3), pp.45~49 (1999)
- S. K. Ayyaswamy, "On graphs whose chromatic transversal number is two", Proyecciones, 30(1), pp.59~64 (2011)
- X.-G. Chen, "Characterization of graphs with equal domination and connected domination numbers", Discrete Math, 289(1-3), pp.129~135 (2004)
- F. Harary, "Graph Theory" (1969), Addison-Wesley
- T. W. Haynes, "Fundamentals of Domination in Graphs" (1998), Marcel Dekker
- T. W. Haynes, "Domination in Graphs, In Advanced Topics" (1998), Marcel Dekker Inc
- L. B. Michaelraj, "A Study on Chromatic Transversal Domination in graphs", 박사, pp.2008
- L. B. Michaelraj, "Chromatic transversal domination in graphs", J. Combin. Math. Combin. Comput, 75, pp.33~40 (2010)