## Abstract The cube polynomial __c__(__G__,__x__) of a graph __G__ is defined as $\sum\nolimits\_{i \ge 0} {\alpha \_i ( G)x^i }$, where ฮฑ~i~(__G__) denotes the number of induced __i__โcubes of __G__, in particular, ฮฑ~0~(__G__) = |__V__(__G__)| and ฮฑ~1~(__G__) = |__E__(__G__)|. Let __G__ be a medi
n-cubes and median graphs
โ Scribed by Martyn Mulder
- Publisher
- John Wiley and Sons
- Year
- 1980
- Tongue
- English
- Weight
- 156 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
Abstract
The nโcube is characterized as a connected regular graph in which for any three vertices u, v, and w there is a unique vertex that lies simultaneously on a shortest (u, v)โpath, a shortest (v, w)โpath, and a shortest (w, u)โpath.
๐ SIMILAR VOLUMES
Hypercubes are characterized among connected bipartite graphs by interval conditions in several ways. These results are based on the following two facts: (i) connected bipartite graphs are median provided that all their intervals induce median graphs, and (ii) median (0, 2)graphs are hypercubes. No
A median graph is called compact if it does not contain an isometric ray. This property is shown to be equivalent to the finite intersection property for convex sets. We show that a compact median graph contains a finite cube that is fixed by all of its automorphisms, and that each family of commuti
## Abstract For each vertex __u__ in a connected graph __H__, the __distance__ of __u__ is the sum of the distances from __u__ to each of the vertices __v__ of __H.__ A vertex of minimum distance in __H__ is called a __median__ vertex. It is shown that for any graph __G__ there exists a graph __H__
## Abstract A cube factorization of the complete graph on __n__ vertices, __K~n~__, is a 3โfactorization of __K~n~__ in which the components of each factor are cubes. We show that there exists a cube factorization of __K~n~__ if and only if __n__ โก 16 (mod 24), thus providing a new family of unifor