New bounds on the hyper-Zagreb index for the simple connected graphs
| Main Authors: | Elumalai, Suresh; Department of Mathematics, Velammal Engineering College, Surapet, Chennai-66, Tamil Nadu, India, Mansour, Toufik; Department of Mathematics, University of Haifa, 3498838 Haifa, Israel, Rostami, Mohammad Ali; Institute for Computer Science, Friedrich Schiller University Jena, Germany |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2018
|
| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/313 https://www.ejgta.org/index.php/ejgta/article/view/313/pdf_72 |
Daftar Isi:
- The hyper-Zagreb index of a simple connected graph G is defined by χ2(G) = ∑uv ∈ E(G)(d(u) + d(v))2. In this paper, we establish, analyze and compare some new upper bounds on the Hyper-Zagreb index in terms of the number of vertices n, number of edges m, maximum vertex degree Δ, and minimum vertex degree δ, first Zagreb index M1(G), second Zagreb index M2(G), harmonic index H(G), and inverse edge degree IED(G). In addition, we give the identities on Hyper-Zagreb index and its coindex for the simple connected graphs.