Eccentric Domination and Restrained Eccentric Domination in Circulant Graphs
نویسندگان
چکیده
منابع مشابه
Domination in Circulant Graphs
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...
متن کاملrestrained roman domination in graphs
a roman dominating function (rdf) on a graph g = (v,e) is defined to be a function satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. a set s v is a restrained dominating set if every vertex not in s is adjacent to a vertex in s and to a vertex in . we define a restrained roman dominating function on a graph g = (v,e) to be ...
متن کاملRestrained domination in unicyclic graphs
Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted by γr(G), is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, th...
متن کاملTotal Domination in Circulant Graphs
Cayley graph is a graph constructed out of a group Γ and a generating set A ⊆ Γ. When Γ = Zn, the corresponding Cayley graph is called as a circulant graph and denoted by Cir(n, A). In this paper, we attempt to find the total domination number of Cir(n, A) for a particular generating set A of Zn and a minimum total dominating set of Cir(n, A). Further, it is proved that Cir(n, A) is 2-total exc...
متن کاملEfficient domination in circulant graphs
Results about wreath products of circulant graphs are used to construct infinitely many circulant graphswith efficient dominating setswhose elements need not be equally spaced in Zn. It is proved that if a circulant graph of large degree has an efficient dominating set, then either its elements are equally spaced, or the graph is the wreath product of a smaller circulant graph with an efficient...
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ژورنال
عنوان ژورنال: International Journal of Engineering Science, Advanced Computing and Bio-Technology
سال: 2018
ISSN: 2249-5592,2249-5584
DOI: 10.26674/ijesacbt/2018/49405