ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory  17(2) (1997)  285-300
DOI: 10.7151/dmgt.1056


Gary Chartrand

Department of Mathematics and Statistics
Western Michigan University, Kalamazoo, MI 49008, USA

Heather Gavlas

Smiths Industries, Defense Systems North America
Grand Rapids, MI 49518-3469, USA

Héctor Hevia

Escuela de Ingenieria Comercial, Universidad Adolfo Ibanez
Balmaceda 1625, Vina del Mar, CHILE

Mark A. Johnson

Pharmacia & Upjohn, 7247-267-133
301 Henrietta Street, Kalamazoo, MI 49007, USA


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 size, G can be j-transformed into H. For every two graphs G and H of the same order and same size, the jump distance dj(G,H) between G and H is defined as the minimum number of edge jumps required to j-transform G into H. The rotation distance dr(G,H) between two graphs G and H of the same order and same size is the minimum number of edge rotations needed to transform G into H. The jump and rotation distances of two graphs of the same order and same size are compared. For a set S of graphs of a fixed order at least 5 and fixed size, the jump distance graph Dj(S) of S has S as its vertex set and where G1 and G2 in S are adjacent if and only if dj(G1,G2) = 1. A graph G is a jump distance graph if there exists a set S of graphs of the same order and same size with Dj(S) = G. Several graphs are shown to be jump distance graphs, including all complete graphs, trees, cycles, and cartesian products of jump distance graphs.

Keywords: edge rotation, rotation distance, edge jump, jump distance, jump distance graph.

1991 Mathematics Subject Classification: Primary: 05C12, Secondary: 05C75.


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