Computational algorithms are described which provide for constructing the set of associated edgeweighted directed graphs such that the average of the characteristic polynomials of the edge-weighted graphs gives the matching polynomial of the parent graph. The weights were chosen to be unities or pur
Matching polynomials of two classes of graphs
โ Scribed by Fu-ji Zhang; Ming-kun Zhou
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 616 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The matching polynomial of a graph has coefficients that give the number ofmatchings in the graph. For a regular graph, we show it is possible to recover the order, degree, girth and number of minimal cycles from the matching polynomial. If a graph is characterized by its matching polynomial, then i
## Let P(G; A) denote the chromatic polynomial of a graph G. G is chromatically unique if G is isomorphic to H for any graph H with P(H; A) = P(G; A). In this paper, we provide two new classes of chromatically unique graphs.
The subdivision threshold for a graph F is the maximum number of edges, ex(n; FS), a graph of order n can have without containing a subdivision of F as a subgraph. We consider two instances: (i) F is the graph formed by a cycle C one vertex of which is adjacent to k vertices not on C, and (ii) F is