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For a given graph $G = (V,E)$, a set $D\subseteq V(G)$ is said to be an outer-connected vertex edge dominating set if $D$ is a vertex edge dominating set and the graph $G \setminus D$ is connected. The outer-connected vertex edge domination number of a graph $G$, denoted by $\gamma _{ve} ^{oc}(G)$, is the cardinality of a minimum outer connected vertex edge dominating set of $G$. We characterize trees $T$ of order $n$ with $l$ leaves, $s$ support vertices, for which $\gamma_{ve}^{oc}(T) = (n-l+s+1)/3$ and also characterize trees with equal domination number and outer-connected vertex edge domination number.
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참고문헌 (6)
참고문헌 신청
R. Boutrig / 2016 / Vertex-edge domination in graphs / Aequationes Math. 90(2):355~366
J. Cyman / 2007 / The outer-connected domination number of a graph / Australas. J. Combin. 38:35~46
T. W. Haynes / 1998 / Fundamentals of Domination in Graphs;Monographs and Textbooks in Pure and Applied Mathematics / Marcel Dekker, Inc. :208
B. Krishnakumari / 2014 / Bounds on the vertex-edge domination number of a tree / C. R. Math. Acad. Sci. Paris 352(5):363~366
J. Lewis / 2010 / Vertex-edge domination / Util. Math. 81:193~213
J. Cyman / 2007 / The outer-connected domination number of a graph / Australas. J. Combin. 38:35~46
T. W. Haynes / 1998 / Fundamentals of Domination in Graphs;Monographs and Textbooks in Pure and Applied Mathematics / Marcel Dekker, Inc. :208
B. Krishnakumari / 2014 / Bounds on the vertex-edge domination number of a tree / C. R. Math. Acad. Sci. Paris 352(5):363~366
J. Lewis / 2010 / Vertex-edge domination / Util. Math. 81:193~213
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