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## Discussiones Mathematicae Graph Theory

1997 | 17 | 2 | 285-300
Tytuł artykułu

### Rotation and jump distances between graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $d_j(G,H)$ between G and H is defined as the minimum number of edge jumps required to j-transform G into H. The rotation distance $d_r(G,H)$ 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 $D_j(S)$ of S has S as its vertex set and where G₁ and G₂ in S are adjacent if and only if $d_j(G₁,G₂) = 1$. A graph G is a jump distance graph if there exists a set S of graphs of the same order and same size with $D_j(S) = G$. Several graphs are shown to be jump distance graphs, including all complete graphs, trees, cycles, and cartesian products of jump distance graphs.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
285-300
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-08-16
poprawiono
1997-07-02
Twórcy
autor
• Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA
autor
• Smiths Industries, Defense Systems North America, Grand Rapids, MI 49518-3469, USA
autor
• Escuela de Ingenieria Comercial, Universidad Adolfo Ibanez, Balmaceda 1625, Vina del Mar, CHILE
autor
• Pharmacia & Upjohn, 7247-267-133, 301 Henrietta Street, Kalamazoo, MI 49007, USA
Bibliografia
• [1] V. Balá, J. Koa, V. Kvasnika and M. Sekanina, A metric for graphs, asopis Pst. Mat. 111 (1986) 431-433.
• [2] G. Benadé, W. Goddard, T.A. McKee and P.A. Winter, On distances between isomorphism classes of graphs, Math. Bohemica 116 (1991) 160-169.
• [3] G. Chartrand, W. Goddard, M.A. Henning, L. Lesniak, H.C. Swart and C.E. Wall, Which graphs are distance graphs? Ars Combin. 29A (1990) 225-232.
• [4] G. Chartrand, F. Saba and H-B Zou, Edge rotations and distance between graphs, asopis Pst. Mat. 110 (1985) 87-91.
• [5] R.J. Faudree, R.H. Schelp, L. Lesniak, A. Gyárfás and J. Lehel, On the rotation distance of graphs, Discrete Math. 126 (1994) 121-135, doi: 10.1016/0012-365X(94)90258-5.
• [6] E.B. Jarrett, Edge rotation and edge slide distance graphs, Computers and Mathematics with Applications, (to appear).
• [7] C. Jochum, J. Gasteiger and I. Ugi, The principle of minimum chemical distance, Angewandte Chemie International 19 (1980) 495-505, doi: 10.1002/anie.198004953.
• [8] M. Johnson, Relating metrics, lines and variables defined on graphs to problems in medicinal chemistry, in: Graph Theory With Applications to Algorithms and Computer Science, Y. Alavi, G. Chartrand, L. Lesniak, D.R. Lick, and C.E. Wall, eds., (Wiley, New York, 1985) 457-470.
• [9] V. Kvasnika and J. Pospichal, Two metrics for a graph-theoretic model of organic chemistry, J. Math. Chem. 3 (1989) 161-191, doi: 10.1007/BF01166047.
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