Open AccessJournal Article
Comparing the Zagreb Indices
Pierre Hansen,Damir Vukičević +1 more
TL;DR: In this article, the first and second Zagreb indices are defined as [GRAPHICS], and it is shown that for all chemical graphs M-1/n <= M-2/m, G is a chemical graph.
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Abstract: Let G = (V, E) be a simple graph with n = vertical bar V vertical bar vertices and m = vertical bar E vertical bar edges ; let d(1), d(2), ..., d(n) denote the degrees of the vertices of G. If Delta = max d(i) <= 4, G is a chemical graph. The first and second Zagreb indices are defined as [GRAPHICS] We show that for all chemical graphs M-1/n <= M-2/m. This does not hold for all general graphs, connected or not.
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Citations
On a novel connectivity index
Bo Zhou,Nenad Trinajstić +1 more
TL;DR: In this paper, the sum-connectivity index for molecular graphs is proposed and several basic properties for this index, especially lower and upper bounds in terms of graph (structural) invariants.
486
A Survey on Comparing Zagreb Indices
Bolian Liu,Zhifu You +1 more
- 01 Jan 2011
TL;DR: The first and second Zagreb indices of a graph G are defined as M1(G) = u∈V d 2 and M2(G), where du denotes the degree of a vertex u in G as discussed by the authors.
62
Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number
Lihua Feng,Aleksandar Ilic +1 more
TL;DR: Sharp bounds are presented for the Zagreb indices, Harary index and hyper-Wiener index of graphs with a given matching number, and the extremal graphs are completely determine.
58
The Zagreb topological indices for a type of Benzenoid systems jagged-rectangle
Wei Gao,Mohammad Reza Farahani +1 more
TL;DR: The Zagreb indices have been introduced more than forty years ago by I. Gutman, and N. Trinajstic and are defined as and in which degree of a vertex u denoted by du as mentioned in this paper.
57
On reformulated Zagreb indices
Aleksandar Ilic,Bo Zhou +1 more
TL;DR: The first and second reformulated Zagreb indices are defined respectively in terms of edge-degrees as EM"1(G)=@?"e"@?"Edeg(e)^2 and EM"2(G)=@?" e"~"fdeg( e)deg(f), where deg(E) denotes the degree of the edge e, and e~f means that the edges e and f are adjacent.
57
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Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons
Ivan Gutman,Nenad Trinajstić +1 more
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