On super vertex-graceful unicyclic graphs

Sin Min Lee; Elo Leung; Ho Kuen Ng

Displaying similar documents to “On super vertex-graceful unicyclic graphs”

The eavesdropping number of a graph

Jeffrey L. Stuart (2009)

Czechoslovak Mathematical Journal

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Let $G$ be a connected, undirected graph without loops and without multiple edges. For a pair of distinct vertices $u$ and $v$ , a minimum ${u, v}$ -separating set is a smallest set of edges in $G$ whose removal disconnects $u$ and $v$ . The edge connectivity of $G$ , denoted $λ (G)$ , is defined to be the minimum cardinality of a minimum ${u, v}$ -separating set as $u$ and $v$ range over all pairs of distinct vertices in $G$ . We introduce and investigate the eavesdropping number, denoted $ε (G)$ , which is defined to be the maximum cardinality...

Classifying trees with edge-deleted central appendage number 2

Shubhangi Stalder, Linda Eroh, John Koker, Hosien S. Moghadam, Steven J. Winters (2009)

Mathematica Bohemica

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The eccentricity of a vertex $v$ of a connected graph $G$ is the distance from $v$ to a vertex farthest from $v$ in $G$ . The center of $G$ is the subgraph of $G$ induced by the vertices having minimum eccentricity. For a vertex $v$ in a 2-edge-connected graph $G$ , the edge-deleted eccentricity of $v$ is defined to be the maximum eccentricity of $v$ in $G - e$ over all edges $e$ of $G$ . The edge-deleted center of $G$ is the subgraph induced by those vertices of $G$ having minimum edge-deleted eccentricity. The edge-deleted...

Radius-invariant graphs

Vojtech Bálint, Ondrej Vacek (2004)

Mathematica Bohemica

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The eccentricity $e (v)$ of a vertex $v$ is defined as the distance to a farthest vertex from $v$ . The radius of a graph $G$ is defined as a $r (G) = {min}_{u \in V (G)} {e (u)}$ . A graph $G$ is radius-edge-invariant if $r (G - e) = r (G)$ for every $e \in E (G)$ , radius-vertex-invariant if $r (G - v) = r (G)$ for every $v \in V (G)$ and radius-adding-invariant if $r (G + e) = r (G)$ for every $e \in E (\bar{G})$ . Such classes of graphs are studied in this paper.