The hamiltonian path graph H(F) of a graph F is that graph having the same vertex set as F and in which two vertices u and u are adjacent if and only if F contains a hamiltonian u -u path. First, in response to a conjecture of Chartrand, Kapoor and Nordhaus, a characterization of nonhamiltonian grap
Path polynomials of a graph
โ Scribed by Ronghua Shi
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 215 KB
- Volume
- 236
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## dedicated to professor w. t. tutte on the occasion of his eightieth birtday It is known that the chromatic number of a graph G=(V, E) with V= [1, 2, ..., n] exceeds k iff the graph polynomial f G => ij # E, i<j (x i &x j ) lies in certain ideals. We describe a short proof of this result, using
The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the elementary properties of this polynomial and compute it for some