W e define a partial ordering on the set of a-polynomials as well as a vertex splitting operation on the set of graphs, and introduce the notions of (r-equivalence and (r- uniqueness of graphs. Let a ( G ) be the a-polynomial of a graph G and a ( G ) = (r(GC). Let H = (G, u , A, 5) be a vertex spli
Equivalence of four descriptions of generalized line graphs
β Scribed by G. R. Vijayakumar
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 284 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
A new characterization of generalized line graphs, analogous to that of line graphs found by Van Rooij and Wilf [Acta Math Acad Sci Hungar 16 (1965), 263-269] is obtained. By a cycle of implications, we settle the equivalence of the definition of generalized line graph given by Hoffman [Combinatorial Structures and their Applications, Gordon and
π SIMILAR VOLUMES
## Abstract Both the line graph and the clique graph are defined as intersection graphs of certain families of complete subgraphs of a graph. We generalize this concept. By a __k__βedge of a graph we mean a complete subgraph with __k__ vertices or a clique with fewer than __k__ vertices. The __k__β
## Abstract All planar connected graphs regular of degree four can be generated from the graph of the octahedron, using four operations.
A relational structure A satisfies the P(n, k) property if whenever the vertex set of A is partitioned into n nonempty parts, the substructure induced by the union of some k of the parts is isomorphic to A. The P(2, 1) property is just the pigeonhole property, (P), introduced by Cameron, and studied