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Rotation and jump distances between graphs

Gary ChartrandHeather GavlasHéctor HeviaMark A. Johnson — 1997

Discussiones Mathematicae Graph Theory

A graph H is obtained from a graph G by an edge rotation if G contains three distinct vertices u,v, and w such that uv ∈ E(G), uw ∉ E(G), and H = G-uv+uw. A graph H is obtained from a graph G by an edge jump if G contains four distinct vertices u,v,w, and x such that uv ∈ E(G), wx∉ E(G), and H = G-uv+wx. If a graph H is obtained from a graph G by a sequence of edge jumps, then G is said to be j-transformed into H. It is shown that for every two graphs G and H of the same order (at least 5) and same...

On strong digraphs with a prescribed ultracenter

Gary ChartrandHeather GavlasKelly SchultzSteven J. Winters — 1997

Czechoslovak Mathematical Journal

The (directed) distance from a vertex u to a vertex v in a strong digraph D is the length of a shortest u - v (directed) path in D . The eccentricity of a vertex v of D is the distance from v to a vertex furthest from v in D . The radius rad D is the minimum eccentricity among the vertices of D and the diameter diam D is the maximum eccentricity. A central vertex is a vertex with eccentricity r a d D and the subdigraph induced by the central vertices is the center C ( D ) . For a central vertex v in a strong digraph...

Stratidistance in stratified graphs

Gary ChartrandHeather GavlasMichael A. HenningReza Rashidi — 1997

Mathematica Bohemica

A graph G is a stratified graph if its vertex set is partitioned into classes (each of which is a stratum or a color class). A stratified graph with k strata is k -stratified. If G is a connected k -stratified graph with strata S i ( 1 i k ) where the vertices of S i are colored X i ( 1 i k ) , then the X i -proximity ρ X i ( v ) of a vertex v of G is the distance between v and a vertex of S i closest to v . The strati-eccentricity s e ( v ) of v is max { ρ X i ( v ) 1 i k } . The minimum strati-eccentricity over all vertices of G is the...

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