The general sum-connectivity index of a graph G is defined as , where d u denotes the degree of vertex u in G, E(G) denotes the edge set of G, and ฮฑ is a real number. We determine the maximum value for the general sum-connectivity indices of n-vertex trees and the corresponding extremal trees for ฮฑ
On the sum-connectivity index of cacti
โ Scribed by Feiying Ma; Hanyuan Deng
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 293 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0895-7177
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๐ SIMILAR VOLUMES
Among the cacti with n vertices and k cycles we determine a unique cactus whose least eigenvalue is minimal. We also explore cacti with n vertices and among them, we find a unique cactus whose least eigenvalue is minimal.
## Abstract We consider four models of random directed multigraphs with __n__ labeled vertices of outโdegree __d__. First we establish formal relationships between our models with respect to exact and asymptotic (as __n__ โ โ) probabilities of possessing a graph monotone property. We also study the
For a digraph G, the kth power G k can be defined in a similar way as in the case of undirected graphs. If G is finite and strongly connected, en(G) := min{k : G k is Hamiltonian} is called the Hamiltonicity exponent of G; analogously, further exponents--for instance, the Hamiltonian connectedness e