Edge Dominating Sets and Vertex Covers

• Autorzy: Ronald Dutton , William F. Klostermeyer
• Języki publikacji: EN

Abstrakty

EN

Bipartite graphs with equal edge domination number and maximum matching cardinality are characterized. These two parameters are used to develop bounds on the vertex cover and total vertex cover numbers of graphs and a resulting chain of vertex covering, edge domination, and matching parameters is explored. In addition, the total vertex cover number is compared to the total domination number of trees and grid graphs.

Słowa kluczowe

EN

edge dominating set; matching; total dominating set; vertex cover

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 2
• Strony: 437-456

Daty

wydano

2013-05-01

online

2013-04-13

Twórcy

autor

Ronald Dutton

• Department of Computer Science University of Central Florida, Orlando, FL, USA,

autor

William F. Klostermeyer

• School of Computing University of North Florida Jacksonville, FL 32224-26 USA,

Bibliografia

• [1] S. Arumugam and S. Velammal, Edge Domination in Graphs, Taiwanese J. Math. 2 (1998) 173-179.
• [2] G. Chatrand, L. Lesniak and P. Zhang, Graphs and Digraphs (Chapman Hall/CRC, 2004).
• [3] R. Dutton, Total vertex covers, Bull. Inst. Combin. Appl., to appear.
• [4] H. Fernau and D.F. Manlove, Vertex and edge covers with clustering properties: complexity and algorithms, in: Algorithms and Complexity in Durham ACID 2006 (King’s College, London, 2006) 69-84.
• [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
• [6] W. Klostermeyer, Some questions on graph protection, Graph Theory Notes N.Y. 57 (2010) 29-33.
• [7] J.R. Lewis, Vertex-edge and edge-vertex parameters in graphs, Ph.D. Disseration (Clemson University, 2007).

Identyfikatory

DOI

10.7151/dmgt.1681