A graph G is n-extendable if it is connected, contains a set of rr independent edges and every set of n-independent edges extends to (i.e. is a subset of) a perfect matching. Combining the results of this and previous papers we answer the question of 2-extendability for all the generalized Petersen
Classifying 2-extendable generalized Petersen graphs
β Scribed by Qinglin Yu
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 559 KB
- Volume
- 103
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
A graph is said to be 2-extendable if any two edges which do not have a common vertex are contained in a l-factor of the graph. In this paper, we show that the generalized Petersen graph GP(n, k) is 2-extandable for all n # 2k or 3k whenever k 2 3, as conjectured by Cammack and Schrag.
π SIMILAR VOLUMES
## Abstract The generalized Petersen graph __GP__ (__n, k__), __n__ β€ 3, 1 β₯ __k__ < __n__/2 is a cubic graph with vertexβset {u~j~; i Ο΅ Z~n~} βͺ {v~j~; i Ο΅ Z~n~}, and edgeβset {u~i~u~i~, u~i~v~i~, v~i~v~i+k, iΟ΅~Z~n~}. In the paper we prove that (i) __GP__(__n, k__) is a Cayley graph if and only if
A graph G is 2-extendable if any two independent edges of G are contained in a perfect matching of G. A Cayley graph of even order over an abelian group is 2-extendable if and only if it is not isomorphic to any of the following circulant graphs: (I) Z2.(1,2n -1), n >~ 3; (II) ZE.(1,2,2n -1,2n -2),
In his paper on the crossing numbers of generalized Petersen graphs, Fiorini proves that P(8, 3) has crossing number 4 and claims at the end that P(10, 3) also has crossing number 4. In this article, we give a short proof of the first claim and show that the second claim is false. The techniques are
The aim of this note is to present a short proof of a result of Nedela and S8 koviera (J. Graph Theory 19 (1995, 1 11)) concerning those generalized Petersen graphs that are also Cayley graphs. In that paper the authors chose the heavy weaponry of regular maps on closed connected orientable surfaces