Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6872189 | Discrete Applied Mathematics | 2014 | 7 Pages |
Abstract
The general sum-connectivity index of a graph G is Ïα(G)=âuvâE(G)(d(u)+d(v))α, where d(u) denotes the degree of vertex uâV(G), and α is a real number. In this paper, we show that in the class of graphs G of order nâ¥3 and minimum degree δ(G)â¥2, the unique graph G having minimum Ïα(G) is K2+Knâ2¯ if â1â¤Î±<α0ââ0.867. Similarly, if we impose the supplementary condition for G to be triangle-free, the extremal graph is K2,nâ2 for nâ¥4 and â1â¤Î±<β0ââ0.817. Since both extremal graphs are 2-connected, it follows that the properties are also true in the subclass of 2-connected graphs.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Ioan Tomescu,