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- W2167880077 abstract "The Merrifield-Simmons index is one of the most popular topological indices in chemistry and in mathematical properties; there is a correlation between this index and boiling points. The MerrifieldSimmons index of a graph is defined as the total number of its independent sets, including the empty set. This paper proposed an edge grafting theorem operation, which is certain kind of edge moving between two vertices distancing one from the unique cycle. Firstly, we define a new graph which is said to be a cycle-r-regular unicycle graph where each vertex in the unique cycle is with degree r. Then we show how the graph of Merrifield-Simmons index changes under the edge grafting operation on the cycle-3-regular unicycle graphs. Finally, we give some applications of these results on ordering the graph of Merrifield-Simmons index among cycle-3-regular unicycle graph. We find that the first three" @default.
- W2167880077 created "2016-06-24" @default.
- W2167880077 creator A5043594742 @default.
- W2167880077 date "2012-01-09" @default.
- W2167880077 modified "2023-09-25" @default.
- W2167880077 title "Ordering a class of unicyclic graphs with respect to Merrifield-Simmons index" @default.
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- W2167880077 doi "https://doi.org/10.5897/ijps11.962" @default.
- W2167880077 hasPublicationYear "2012" @default.
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