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 ∈ V ( G ) { e ( u ) } . A graph G is radius-edge-invariant if r ( G - e ) = r ( G ) for every e ∈ E ( G ) , radius-vertex-invariant if r ( G - v ) = r ( G ) for every v ∈ V ( G ) and radius-adding-invariant if r ( G + e ) = r ( G ) for every e ∈ E ( G ¯ ) . Such classes of graphs are studied in this paper.