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Rotation and jump distances between graphs

Gary Chartrand; Heather Gavlas; Héctor Hevia; Mark 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 Chartrand; Heather Gavlas; Kelly Schultz; Steven 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...

On signed degrees in signed graphs

Gary Chartrand; Heather Gavlas; Frank Harary; Michelle Schultz — 1994

Czechoslovak Mathematical Journal

Stratidistance in stratified graphs

Gary Chartrand; Heather Gavlas; Michael A. Henning; Reza 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 $S_{i}$ $(1 \leq i \leq k)$ where the vertices of $S_{i}$ are colored $X_{i}$ $(1 \leq i \leq k)$ , 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 $max {ρ_{X_{i}} (v) ∣ 1 \leq i \leq k}$ . The minimum strati-eccentricity over all vertices of $G$ is the...

Skolem-type difference sets for cycle systems.

Bryant, Darryn; Gavlas, Heather; Ling, Alan C.H. — 2003

The Electronic Journal of Combinatorics [electronic only]

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