Counting double covers of graphs
β Scribed by M. Hofmeister
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 288 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Any group of automorphisms of a graph G induces a notion of isomorphism between double covers of G. The corresponding isomorphism classes will be counted.
π SIMILAR VOLUMES
Let 1 be a distance-regular graph of diameter d and valency k>2. If b t =1 and 2t d, then 1 is an antipodal double-cover. Consequently, if f >2 is the multiplicity of an eigenvalue of the adjacency matrix of 1 and if 1 is not an antipodal doublecover then d 2f&3. This result is an improvement of God
Some new results on minimum cycle covers are proved. As a consequence, it is obtained that the edges of a bridgeless graph G can be covered by cycles of total length at most |E(G)| + 25 24 (|V (G)| -1), and at most |E(G)| + |V (G)| -1 if G contains no circuit of length 8 or 12.
Let (G, w ) denote a simple graph G with a weight function w : β¬(G) -{0,1,2}. A path cover of (G, w ) is a collection of paths in G such that every edge e is contained in exactly w(e) paths of the collection. For a vertex u , w ( v ) is the sum of the weights of the edges incident with U ; U is call
## Abstract We prove in this paper that every simple graph __G__ admits a perfect path double cover (PPDC), i.e., a set of paths of __G__ such that each edge of __G__ belongs to exactly two of the paths and each vertex of __G__ is an end of exactly two of the paths, where a path of length zero is c
## Abstract Let __G__ be a bridgeless cubic graph. We prove that the edges of __G__ can be covered by circuits whose total length is at most (44/27) |__E(G)__|, and if Tutte's 3βflow Conjecture is true, at most (92/57) |__E(G)__|.