A note on on-line ranking number of graphs

Gabriel Semanišin; Roman Soták

Displaying similar documents to “A note on on-line ranking number of graphs”

Induced-paired domatic numbers of graphs

Bohdan Zelinka (2002)

Mathematica Bohemica

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A subset $D$ of the vertex set $V (G)$ of a graph $G$ is called dominating in $G$ , if each vertex of $G$ either is in $D$ , or is adjacent to a vertex of $D$ . If moreover the subgraph $< D >$ of $G$ induced by $D$ is regular of degree 1, then $D$ is called an induced-paired dominating set in $G$ . A partition of $V (G)$ , each of whose classes is an induced-paired dominating set in $G$ , is called an induced-paired domatic partition of $G$ . The maximum number of classes of an induced-paired domatic partition of $G$ is the induced-paired...

On integral sum graphs with a saturated vertex

Zhibo Chen (2010)

Czechoslovak Mathematical Journal

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As introduced by F. Harary in 1994, a graph $G$ is said to be an $i n t e g r a l$ $s u m$ $g r a p h$ if its vertices can be given a labeling $f$ with distinct integers so that for any two distinct vertices $u$ and $v$ of $G$ , $u v$ is an edge of $G$ if and only if $f (u) + f (v) = f (w)$ for some vertex $w$ in $G$ . We prove that every integral sum graph with a saturated vertex, except the complete graph $K_{3}$ , has edge-chromatic number equal to its maximum degree. (A vertex of a graph $G$ is said to be if it is adjacent to every...

Homogeneously embedding stratified graphs in stratified graphs

Gary Chartrand, Donald W. Vanderjagt, Ping Zhang (2005)

Mathematica Bohemica

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A 2-stratified graph $G$ is a graph whose vertex set has been partitioned into two subsets, called the strata or color classes of $G$ . Two $2$ -stratified graphs $G$ and $H$ are isomorphic if there exists a color-preserving isomorphism $φ$ from $G$ to $H$ . A $2$ -stratified graph $G$ is said to be homogeneously embedded in a $2$ -stratified graph $H$ if for every vertex $x$ of $G$ and every vertex $y$ of $H$ , where $x$ and $y$ are colored the same, there exists an induced $2$ -stratified subgraph $H^{'}$ of $H$ containing $y$ and a color-preserving...