نتایج جستجو برای: domination polynomial

تعداد نتایج: 104573  

Journal: :Discussiones Mathematicae Graph Theory 2010
Ermelinda DeLaViña Ryan Pepper Bill Waller

In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least two-thirds of the radius of the graph, three times the domination number is at least two more than the number of cut-vertices in the graph, and the domination number of a tree is at least as large as the minimum order of a maximal matc...

2009
Nader Jafari Rad

A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G− v is less than the total domination number of G. We call these graphs γt-critical. In this paper, we determine the domination and the total domination number in the Circulant graphs Cn〈1, 3〉, and then study γ-criticality...

2014
P. Pradhan B. S. Rawat

Harary, F. , 1997 Graph Theory, Narosa Publishing House. Arumugam, S. , Joseph, J. P. 1999 On graphs with equal domination and connected domination numbers, Discrete Mathematics vol. 206, 45-49. Deo, N. 2005 Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall of India Private Limited. Saoud, M. , Jebran, J. 2009 Finding A Minimum Dominating Set by Transforming Domi...

2015
C. Natarajan S. K. Ayyaswamy

Let G = (V,E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V − S, there exists u ∈ S such that d(u, v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γh(G). In this paper we characterize the family of trees and unicyclic graphs for which γh(G) = γt(G) and γh(G) = γc(G) where γt(G) and γc(G) are the ...

Journal: :Discrete Applied Mathematics 2012
Yair Caro Michael A. Henning

A directed dominating set in a directed graph D is a set S of vertices of V such that every vertex u ∈ V (D) \ S has an adjacent vertex v in S with v directed to u. The directed domination number of D, denoted by γ(D), is the minimum cardinality of a directed dominating set in D. The directed domination number of a graph G, denoted Γd(G), which is the maximum directed domination number γ(D) ove...

Journal: :Australasian J. Combinatorics 2003
Igor E. Zverovich

We prove that, for each p ≥ 1, there exists a polynomial time algorithm for finding a minimum domination set in the class of all (Kp, P5)-free graphs. Let G be a graph with vertex-set V (G) and edge-set E(G). The notation x ∼ y (respectively, x 6∼ y) means that vertices x, y ∈ V (G) are adjacent (respectively, non-adjacent). Moreover, if X ⊆ V (G) and y ∈ V (G)\X, we write y ∼ X (respectively, ...

Journal: :Australasian J. Combinatorics 2010
B. Sharada Nandappa D. Soner

A set D of vertices of a graph G is a dominating set 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 of G. The domination subdivision number of G is the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the domination number. Arumugam h...

2002
F. R. Hsu M. K. Shan

A connected domination set of a graph is a set of vertices such that every vertex not in is adjacent to and the induced subgraph of is connected. The minimum connected domination set of a graph is the connected domination set with the minimum number of vertices. In this paper, we propose parallel algorithms for finding the minimum connected domination set of interval graphs and circular-arc gra...

2014
M S Sunitha

In this paper we introduce the concept of strong total domination in fuzzy graphs. We determine the strong total domination number for several classes of fuzzy graphs. A lower bound and an upper bound for the strong total domination number in terms of strong domination number is obtained. Strong total domination in fuzzy trees is studied. A necessary and sufficient condition for the set of fuzz...

Journal: :Discrete Mathematics 2004
Peter Dankelmann Gayla S. Domke Wayne Goddard Paul J. P. Grobler Johannes H. Hattingh Henda C. Swart

We find the maximum number of edges for a graph of given order and value of parameter for several domination parameters. In particular, we consider the total domination and independent domination numbers.

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