The cobondage number of a graph

• Autorzy: V.R. Kulli , B. Janakiram
• Języki publikacji: EN

Abstrakty

EN

A set D of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V-D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. We define the cobondage number $b_c(G)$ of G to be the minimum cardinality among the sets of edges X ⊆ P₂(V) - E, where P₂(V) = {X ⊆ V:|X| = 2} such that γ(G+X) < γ(G). In this paper, the exact values of b_c(G) for some standard graphs are found and some bounds are obtained. Also, a Nordhaus-Gaddum type result is established.

Słowa kluczowe

EN

graph; domination number; cobondage number

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1996
• Tom: 16
• Numer: 2
• Strony: 111-117

Daty

wydano

1996

otrzymano

1995-01-18

poprawiono

1996-09-25

Twórcy

autor

V.R. Kulli

• Department of Mathematics, Gulbarga University, Gulbarga-585 106, India

autor

B. Janakiram

• Department of Mathematics, Gulbarga University, Gulbarga-585 106, India

Bibliografia

• [1] E.J. Cockayne and S.T. Hedetniemi, Domination of undirected graphs - A survey, In: Theory and Applications of Graphs (Lecture Notes in Math. 642, Spring-Verlag, 1978) 141-147.
• [2] J.F. Fink, M.S. Jakobson, L.F. Kinch and J. Roberts, The bondage number of a graph, Discrete Math. 86 (1990) 47-57, doi: 10.1016/0012-365X(90)90348-L.
• [3] F. Harary, Graph Theory (Addison-Wesley, Reading Mass., 1969).
• [4] E.A. Nordhaus and J.W. Gaddum, On complementary graphs, Amer. Math. Monthly 63 (1956) 175-177, doi: 10.2307/2306658.

Identyfikatory

DOI

10.7151/dmgt.1026