Resolution of AutoGraphiX conjectures relating the index and matching number of graphs
✍ Scribed by Dragan Stevanović
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 131 KB
- Volume
- 433
- Category
- Article
- ISSN
- 0024-3795
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📜 SIMILAR VOLUMES
## Abstract We prove that __m__ ≤ Δ (__n__ − γ~t~) for every graph each component of which has order at least 3 of order __n__, size __m__, total domination number γ~t~, and maximum degree Δ ≥ 3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 285–290, 2005
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
## Abstract The proof of the main theorem in the paper [1] is incorrect as it is missing an important case. Here we complete the proof by giving the missing case. © 2007 Wiley Periodicals, Inc. J Graph Theory 54: 350–353, 2007