On the Game Domination Number of Graphs with Given Minimum Degree
نویسندگان
چکیده
منابع مشابه
On Independent Domination Number of Graphs with given Minimum Degree
We prove a new upper bound on the independent domination number of graphs in terms of the number of vertices and the minimum degree. This bound is slightly better than that by J. Haviland 3] and settles Case = 2 of the corresponding conjecture by O. Favaron 2].
متن کاملOn the Game Domination Number of Graphs with Given Minimum Degree
In the domination game, introduced by Brešar, Klavžar, and Rall in 2010, Dominator and Staller alternately select a vertex of a graph G. A move is legal if the selected vertex v dominates at least one new vertex – that is, if we have a u ∈ N [v] for which no vertex from N [u] was chosen up to this point of the game. The game ends when no more legal moves can be made, and its length equals the n...
متن کاملDiameter Two Graphs of Minimum Order with Given Degree Set
The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...
متن کاملOn the independent domination number of graphs with given minimum degree
We prove a new upper bound on the independent domination number of graphs in terms of the number of vertices and the minimum degree. This bound is slightly better than that of Haviland (1991) and settles the case 6 = 2 of the corresponding conjecture by Favaron (1988). @ 1998 Elsevier Science B.V. All rights reserved
متن کاملOn the super domination number of graphs
The open neighborhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $Dsubseteq V(G)$, we define $overline{D}=V(G)setminus D$. A set $Dsubseteq V(G)$ is called a super dominating set of $G$ if for every vertex $uin overline{D}$, there exists $vin D$ such that $N(v)cap overline{D}={u}$. The super domination number of $G$ is the minimum car...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/4497