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Displaying similar documents to “Functigraphs: An extension of permutation graphs”

Cores and shells of graphs

Allan Bickle (2013)

Mathematica Bohemica

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The k -core of a graph G , C k ( G ) , is the maximal induced subgraph H G such that δ ( G ) k , if it exists. For k > 0 , the k -shell of a graph G is the subgraph of G induced by the edges contained in the k -core and not contained in the ( k + 1 ) -core. The core number of a vertex is the largest value for k such that v C k ( G ) , and the maximum core number of a graph, C ^ ( G ) , is the maximum of the core numbers of the vertices of G . A graph G is k -monocore if C ^ ( G ) = δ ( G ) = k . This paper discusses some basic results on the structure of k -cores and...

On ( 4 , 1 ) * -choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles

Haihui Zhang (2013)

Commentationes Mathematicae Universitatis Carolinae

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A graph G is called ( k , d ) * -choosable if for every list assignment L satisfying | L ( v ) | = k for all v V ( G ) , there is an L -coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this paper, it is proved that every toroidal graph without chordal 7-cycles and adjacent 4-cycles is ( 4 , 1 ) * -choosable.

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...