Factor-critical property in 3-dominating-critical graphs

Factor-critical property in 3-dominating-critical graphs

Let γ(G) be the domination number of a graph G. A graph G is domination-vertex-critical, or γ-vertex-critical, if γ(G− v) < γ(G) for every vertex v ∈ V (G). In this paper, we show that: Let G be a γ-vertex-critical graph and γ(G) = 3. (1) If G is of even order and K1,6-free, then G has a perfect matching; (2) If G is of odd order and K1,7-free, then G has a near perfect matching with only three...

Matching and Factor-Critical Property in 3-Dominating-Critical Graphs∗

Let γ(G) be the domination number of a graphG. A graphG is dominationvertex-critical, or γ-vertex-critical, if γ(G − v) < γ(G) for every vertex v ∈ V(G). In this paper, we show that: Let G be a γ-vertex-critical graph and γ(G) = 3. (1) If G is of even order and K1,6-free, then G has a perfect matching; (2) If G is of odd order and K1,7-free, then G has a near perfect matching with only three ex...

m at h . C O ] 2 8 A ug 2 00 6 Factor - Critical Property in 3 - Dominating - Critical Graphs ∗

A vertex subset S of a graph G is a dominating set if every vertex of G either belongs to S or is adjacent to a vertex of S. The cardinality of a smallest dominating set is called the dominating number of G and is denoted by γ(G). A graph G is said to be γ-vertex-critical if γ(G− v) < γ(G), for every vertex v in G. Let G be a 2-connected K1,5-free 3-vertex-critical graph. For any vertex v ∈ V (...

Dominating Critical in Intuitionistic Fuzzy Graphs

Let G be an IFG. Then V D  is said to bae a strong (weak) dominating set if every D V v   is strongly (weakly) dominated by some vertex in D. We denote the strong (weak) intuitionistic fuzzy dominating set by sid-set (wid-set). The minimum vertex cardinality over all the sid-set (wid-set) is called the strong (weak) dominating number of an IFG and is denoted by )] ( [ ) ( G G wid sid   In ...

Dominating Critical in Intuitionistic Fuzzy Graphs