A conjecture on benzenoid graphs
β Scribed by J. Cioslowski
- Publisher
- Springer
- Year
- 1991
- Tongue
- English
- Weight
- 26 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0259-9791
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let K~ ) be the umon of two complete graphs on n vertices which have preosely one vertex in common. Graham and Sloane have shown that K~ ~ is not harmomous for n od:~, /(~,~ is harmonious, and K~62~ is not harmonious. They also conjecture that K~' t,, not h,~rmomous except for n = 4. Here, it Is sho
The resonance graph of a benzenoid graph G has the 1-factors of G as vertices, two 1-factors being adjacent if their symmetric difference forms the edge set of a hexagon of G. It is proved that the smallest number of elementary cuts that cover a catacondensed bensenoid graph equals the dimension of
For any graph H, the function h,. defined by setting h,(G) equal to the number of homomorphisms from G into H, is a multiplicative increasing function. L.ov&sz [2] has asked whether ail nonzero multiplicative increasing functions are generated by functions of this type. We show that this is not the
## Abstract Gol'dberg has recently constructed an infinite family of 3βcritical graphs of even order. We now prove that if there exists a __p__(β₯4)βcritical graph __K__ of odd order such that __K__ has a vertex __u__ of valency 2 and another vertex __v__ β __u__ of valency β€(__p__ + 2)/2, then ther