The Hosoya index and the Merrifield-Simmons index of a graph are defined as the total number of the matchings (including the empty edge set) and the total number of the independent vertex sets (including the empty vertex set) of the graph, respectively. Let W n,k be the set of connected graphs with
Cacti with the maximum Merrifield–Simmons index and given number of cut edges
✍ Scribed by Maolin Wang
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 286 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0893-9659
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📜 SIMILAR VOLUMES
Let G be a connected and simple graph, and let i(G) denote the number of stable sets in G. In this letter, we have presented a sharp upper bound for the i(G)-value among the set of graphs with k cut edges for all possible values of k, and characterized the corresponding extremal graphs as well.
The interval number of a graph G, denoted i(G), is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t compact real intervals. It is known that every planar graph has interval number at most 3 and that this result is best possible. We investiga