On the cycle space of graphs
β Scribed by Bojan Mohar
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 68 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0012-365X
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## Abstract Let __G__ be a connected graph with edge set __E__ embedded in the surface β. Let __G__Β° denote the geometric dual of __G__. For a subset __d__ of __E__, let Ο__d__ denote the edges of __G__Β° that are dual to those edges of __G__ in __d__. We prove the following generalizations of wellβ
## Abstract This paper considers conditions ensuring that cycleβisomorphic graphs are isomorphic. Graphs of connectivity β©Ύ 2 that have no loops were studied in [2] and [4]. Here we characterize all graphs __G__ of connectivity 1 such that every graph that is cycleβisomorphic to __G__ is also isomor
## Abstract Bonnington and Richter defined the cycle space of an infinite graph to consist of the sets of edges of subgraphs having even degree at every vertex. Diestel and KΓΌhn introduced a different cycle space of infinite graphs based on allowing infinite circuits. A more general point of view w
Tan, E.L., Some notes on cycle graphs, Discrete Mathematics 105 (1992) 221-226. The cycle graph C(G) of a graph G is the graph whose vertices are the chordless cycles of G and two vertices in C(G) are adjacent whenever the corresponding chordless cycles have at least one edge in common. If G is acyc