On Well-Edge-Dominated Graphs
نویسندگان
چکیده
A graph is said to be well-edge-dominated if all its minimal edge dominating sets are minimum. It known that every G also equimatchable, meaning maximal matching in maximum. In this paper, we show a connected, triangle-free, nonbipartite, graph, then one of three graphs. We characterize the split graphs and Cartesian products. particular, connected product $$G\Box H$$ well-edge-dominated, where H have order at least 2, only = K_2 \Box K_2$$ . prove two nontrivial it equimatchable.
منابع مشابه
Locally Well-Dominated and Locally Independent Well-Dominated Graphs
In this article we present characterizations of locally well-dominated graphs and locally independent well-dominated graphs, and a sufficient condition for a graph to be k-locally independent well-dominated. Using these results we show that the irredundance number, the domination number and the independent domination number can be computed in polynomial time within several classes of graphs, e....
متن کاملOn (Semi-) Edge-primality of Graphs
Let $G= (V,E)$ be a $(p,q)$-graph. A bijection $f: Eto{1,2,3,ldots,q }$ is called an edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ where $f^+(u) = sum_{uwin E} f(uw)$. Moreover, a bijection $f: Eto{1,2,3,ldots,q }$ is called a semi-edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ or $f^+(u)=f^+(v)$. A graph that admits an ...
متن کاملWell-dominated graphs without cycles of lengths 4 and 5
Let G be a graph. A set S of vertices in G dominates the graph if every vertex of G is either in S or a neighbor of a vertex in S. Finding a minimal cardinality set which dominates the graph is an NP-complete problem. The graph G is well-dominated if all its minimal dominating sets are of the same cardinality. The complexity status of recognizing well-dominated graphs is not known. We show that...
متن کاملOn Edge-colouring Indiierence Graphs on Edge-colouring Indiierence Graphs
Vizing's theorem states that the chromatic index 0 (G) of a graph G is either the maximum degree (G) or (G) + 1. A graph G is called overfull if jE(G)j > (G)bjV (G)j=2c. A suu-cient condition for 0 (G) = (G)+1 is that G contains an overfull subgraph H with (H) = (G). Plantholt proved that this condition is necessary for graphs with a universal vertex. In this paper, we conjecture that, for indi...
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
ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2022
ISSN: ['1435-5914', '0911-0119']
DOI: https://doi.org/10.1007/s00373-022-02508-9