Iranian journal of mathemathical chemistry./Iranian journal of mathemathical chemistry· 2013Q2
THE HYPER-ZAGREB INDEX OF GRAPH OPERATIONS
- 353citations
- Q2SCImago
- 2013year
Short summary
A new graph invariant, the Hyper-Zagreb index, is defined as the sum of the squares of the sums of degrees of adjacent vertices, and its values are computed for Cartesian products, compositions, joins, and disjunctions of graphs.
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Key points
- The Hyper-Zagreb index is defined as HM(G) = Σ_uv∈E(G) (deg(u) + deg(v))^2.
- Formulas for the Hyper-Zagreb index are derived for graph operations.
- The operations studied include Cartesian product, composition, join, and disjunction of graphs.
AI-generated from the title and abstract; the full text is not read.
Abstract
Let G be a simple connected graph. The first and second Zagreb indices have been introduced as vV(G) (v)2 M1(G) degG and M2(G) uvE(G)degG(u)degG(v) , respectively, where degG v(degG u) is the degree of vertex v (u) . In this paper, we define a new distance-based named HyperZagreb as e uv E(G) . (v))2 HM(G) (degG(u) degG In this paper, the HyperZagreb index of the Cartesian product, composition, join and disjunction of graphs are computed.
The authors' abstract, as published at the source. Iranian journal of mathemathical chemistry./Iranian journal of mathemathical chemistry, 2013 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics