A Note on Total and Paired Domination of Cartesian Product Graphs
نویسندگان
چکیده
منابع مشابه
A Note on Total and Paired Domination of Cartesian Product Graphs
A dominating set D for a graph G is a subset of V (G) such that any vertex not in D has at least one neighbor in D. The domination number γ(G) is the size of a minimum dominating set in G. Vizing’s conjecture from 1968 states that for the Cartesian product of graphs G and H, γ(G)γ(H) ≤ γ(G H), and Clark and Suen (2000) proved that γ(G)γ(H) ≤ 2γ(G H). In this paper, we modify the approach of Cla...
متن کاملA Note on Integer Domination of Cartesian Product Graphs
Given a graph G, a dominating set D is a set of vertices such that any vertex in G has at least one neighbor (or possibly itself) in D. A {k}-dominating multiset Dk is a multiset of vertices such that any vertex in G has at least k vertices from its closed neighborhood in Dk when counted with multiplicity. In this paper, we utilize the approach developed by Clark and Suen (2000) and properties ...
متن کاملA Note on Total Domination Critical Graphs
The total domination number of G denoted by γt(G) is the minimum cardinality of a total dominating set of G. A graph G is total domination vertex critical or just γt-critical, if for any vertex v of G that is not adjacent to a vertex of degree one, γt(G − v) < γt(G). If G is γt-critical and γt(G) = k, then G is k-γt-critical. Haynes et al [The diameter of total domination vertex critical graphs...
متن کاملInteger domination of Cartesian product graphs
Given a graph G, a dominating set D is a set of vertices such that any vertex not in D has at least one neighbor in D. A {k}-dominating multiset Dk is a multiset of vertices such that any vertex in G has at least k vertices from its closed neighborhood in Dk when counted with multiplicity. In this paper, we utilize the approach developed by Clark and Suen (2000) to prove a ‘‘Vizing-like’’ inequ...
متن کاملTotal domination of Cartesian products of graphs
Let γt(G) and γpr(G) denote the total domination and the paired domination numbers of graph G, respectively, and let G ¤ H denote the Cartesian product of graphs G and H. In this paper, we show that γt(G)γt(H) ≤ 5γt(G ¤ H), which improves the known result γt(G)γt(H) ≤ 6γt(G ¤ H) given by Henning and Rall.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/2535