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Displaying similar documents to “The eavesdropping number of a graph”

Paths with restricted degrees of their vertices in planar graphs

Stanislav Jendroľ (1999)

Czechoslovak Mathematical Journal

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In this paper it is proved that every 3 -connected planar graph contains a path on 3 vertices each of which is of degree at most 15 and a path on 4 vertices each of which has degree at most 23 . Analogous results are stated for 3 -connected planar graphs of minimum degree 4 and 5 . Moreover, for every pair of integers n 3 , k 4 there is a 2 -connected planar graph such that every path on n vertices in it has a vertex of degree k .

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...

On super vertex-graceful unicyclic graphs

Sin Min Lee, Elo Leung, Ho Kuen Ng (2009)

Czechoslovak Mathematical Journal

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A graph G with p vertices and q edges, vertex set V ( G ) and edge set E ( G ) , is said to be super vertex-graceful (in short SVG), if there exists a function pair ( f , f + ) where f is a bijection from V ( G ) onto P , f + is a bijection from E ( G ) onto Q , f + ( ( u , v ) ) = f ( u ) + f ( v ) for any ( u , v ) E ( G ) , Q = { ± 1 , , ± 1 2 q } , if q is even, { 0 , ± 1 , , ± 1 2 ( q - 1 ) } , if q is odd, and P = { ± 1 , , ± 1 2 p } , if p is even, { 0 , ± 1 , , ± 1 2 ( p - 1 ) } , if p is odd. We determine here families of unicyclic graphs that are super vertex-graceful.