## Abstract A graph __G__ is __k__βordered if for every ordered sequence of __k__ vertices, there is a cycle in __G__ that encounters the vertices of the sequence in the given order. We prove that if __G__ is a connected graph distinct from a path, then there is a number __t~G~__ such that for ever
Characterizations of second iterated line graphs
β Scribed by Zhao Guangfu
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 477 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract The clique graph __K__(__G__) of a graph is the intersection graph of maximal cliques of __G.__ The iterated clique graph __K__^__n__^(__G__) is inductively defined as __K__(K^nβ1^(__G__)) and __K__^1^(__G__) = __K__(__G__). Let the diameter diam(__G__) be the greatest distance between
## Abstract The possible classes of balanced circles of a signed graph are characterized in two ways.
In this paper all connected line graphs whose second largest eigenvalue does not exceed 1 are characterized. Besides, all minimal line graphs with second largest eigenvalue greater than 1 are determined.
## Abstract New characterizations of triangulated and cotriangulated graphs are presented. Cotriangulated graphs form a natural subclass of the class of strongly perfect graphs, and they are also characterized in terms of the shellability of some associated collection of sets. Finally, the notion o
## Abstract In this paper we prove that for a simple graph __G__ without isolated vertices 0 < Ξ»~2~(__G__) < 1/3 if and only if __G__ β KΜ~__n__β3~ V (__K__~1~ βͺ __K__~2~), the graph obtained by joining each vertex of KΜ~__n__β3~ to each vertex of __K__~1~ βͺ __K__~2~). Β© 1993 John Wiley & Sons, Inc