Clique polynomials and independent set polynomials of graphs
β Scribed by Cornelis Hoede; Xueliang Li
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 492 KB
- Volume
- 125
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
This paper introduces two kinds of graph polynomials, clique polynomial and independent set polynomial.
The paper focuses on expansions of these polynomials. Some open problems are mentioned.
π SIMILAR VOLUMES
The tension polynomial F G (k) of a graph G, evaluating the number of nowhere-zero Z k -tensions in G, is the nontrivial divisor of the chromatic polynomial G (k) of G, in that G (k) ΒΌ k c(G) F G (k), where c(G) denotes the number of components of G. We introduce the integral tension polynomial I G
It is shown in this note that it can be recognized in polynomial time whether the vertex set of a finite undirected graph can be partitioned into one or two independent sets and one or two cliques. Such graphs generalize bipartite and split graphs and the result also shows that it can be recognized
## Abstract This paper is mainly concerned with classes of simple graphs with exactly __c__ connected components, __n__ vertices and __m__ edges, for fixed __c,n,m__ β β. We find an optimal lower bound for the __i__th coefficient of the chromatic polynomial of a graph in such a class and also an op