A graph G is 3-γ-critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Wojcicka conjectured that every 3-γ-critical graph ...
The graph G is 3-γ-critical if γ = 3 and the addition of any edge decreases γ by 1. It was conjectured that any connected 3-γ-critical graph with δ ⩾ 2 is ...
Oct 22, 2024 · PDF | A graph G is 3-γ-critical if its domination number γ is 3 and the addition of any edge decreases γ by 1.
Oct 22, 2024 · The graph G is 3-γ-critical if γ = 3 and the addition of any edge decreases γ by 1. It was conjectured that any connected 3-γ-critical graph ...
We prove that every $2$-connected $3$-$\gamma$-vertex critical claw-free graph is Hamiltonian and the condition claw-free is necessary. For $k$-$\gamma_{c}$- ...
In this paper, we show that a $3$-$\gamma_{c}$-critical graph $G$ satisfies $\alpha \leq \kappa + 2$. Moreover, if $\kappa \geq 3$, then $\alpha = \kappa + p$ ...
Furthermore, we prove that 3-connected uniquely hamiltonian 4-regular graphs exist if and only if 2-connected uniquely hamiltonian 4-regular graphs exist.
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Jun 20, 2019 · In this section, we show that, for k ≥ 4 and k − 3 ≤ ζ ≤ k − 2, every k-γc-critical graph with ζ cut-vertices contains a hamiltonian path. We ...
A graph G is 3-domination critical if its domination number is 3 and the addition of any edge decreases by 1. Let G be a 3-connected 3-domination critical ...
Dec 22, 2011 · Abstract. A graph G is said to be 3-domination critical if its domination number γ(G) = 3 and γ(G + e) = 2 for any edge e not contained in G.