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...