Edge dominating sets and vertex covers
نویسندگان
چکیده
Bipartite graphs with equal edge domination number and maximum matching cardinality are characterized. These two parameters are used to develop bounds on the vertex cover and total vertex cover numbers of graphs and a resulting chain of vertex covering, edge domination, and matching parameters is explored. In addition, the total vertex cover number is compared to the total domination number of trees and grid graphs.
منابع مشابه
On the edge geodetic and edge geodetic domination numbers of a graph
In this paper, we study both concepts of geodetic dominatingand edge geodetic dominating sets and derive some tight upper bounds onthe edge geodetic and the edge geodetic domination numbers. We also obtainattainable upper bounds on the maximum number of elements in a partitionof a vertex set of a connected graph into geodetic sets, edge geodetic sets,geodetic domin...
متن کاملParameterized Edge Dominating Set in Cubic Graphs
In this paper, we present an improved algorithm to decide whether a graph of maximum degree 3 has an edge dominating set of size k or not, which is based on enumerating vertex covers. We first enumerate vertex covers of size at most 2k and then construct an edge dominating set based on each vertex cover to find a satisfied edge dominating set. To enumerate vertex covers, we use a branch-and-red...
متن کاملStrength of strongest dominating sets in fuzzy graphs
A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...
متن کاملTwo Minimum Dominating Sets with Minimum Intersection in Chordal Graphs
We prove that the problem of nding two minimum dominating sets (connected dominating sets or vertex clique covers) with minimum intersection is linearly solvable in interval graphs. Furthermore, the problem of deciding whether or not there exist two disjoint minimum dominating sets (connected dominating sets or vertex clique covers) is shown to be NP-hard for chordal graphs.
متن کاملOn the signed Roman edge k-domination in graphs
Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 33 شماره
صفحات -
تاریخ انتشار 2013