## Defining set The defining number The strong defining number Harary graph a b s t r a c t In a given graph G = (V , E), a set of vertices S with an assignment of colors to them is said to be a defining set of the vertex coloring of G if there exists a unique extension of the colors of S to a c
Additively weighted Harary index of some composite graphs
✍ Scribed by Yaser Alizadeh; Ali Iranmanesh; Tomislav Došlić
- Book ID
- 119227557
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 230 KB
- Volume
- 313
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Eliasi and Taeri [Extension of the Wiener index and Wiener polynomial, Appl. Math. Lett. 21 (2008) 916-921] introduced the notion of y-Wiener index of graphs as a generalization of the classical Wiener index and hyper Wiener index of graphs. They obtained some mathematical properties of this new def
The level of a vertex in a rooted graph is one more than its distance from the root vertex. A generalized Bethe tree is a rooted tree in which vertices at the same level have the same degree. We characterize completely the eigenvalues of the Laplacian, signless Laplacian and adjacency matrices of a
of length m in G and d, denotes the degre,e of the vertex i. We find upper bounds for "z(G) using the eigenvalues of the Laplaci~.m matrix of an associated weighted graph.