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On the 3-$gamma_t$-Critical Graphs of Order $Delta(G)+3$ | | Haoli Wang
; Xirong Xu
; Yang Yuansheng
; Lei Wang
; | | Date: |
12 Mar 2011 | | Abstract: | Let $gamma_t(G)$ be the total domination number of graph $G$, a graph $G$ is
$k$-total domination vertex critical (or just $k$-$gamma_t$-critical) if
$gamma_t(G)=k$, and for any vertex $v$ of $G$ that is not adjacent to a vertex
of degree one, $gamma_t(G-v)=k-1$. Mojdeh and Rad cite{MR06} proposed an open
problem: Does there exist a 3-$gamma_t$-critical graph $G$ of order
$Delta(G)+3$ with $Delta(G)$ odd? In this paper, we prove that there exists a
3-$gamma_t$-critical graph $G$ of order $Delta(G)+3$ with odd $Delta(G)geq
9$. | | Source: | arXiv, 1103.2415 | | Services: | Forum | Review | PDF | Favorites | |
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