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For a graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. This paper investigates the Zagreb indices of unicyclic graphs by introducing some transformations, and characterize the unicyclic graphs… (More)

- Lixing Xu, Shubo Chen
- Appl. Math. Lett.
- 2008

The PI index is a graph invariant defined as the summation of the sums of neu(e|G) and nev(e|G) over all the edges e = uv of a connected graph G, i.e., PI(G) = ∑ e∈E(G)[neu(e|G)+ nev(e|G)], where neu(e|G) is the number of edges of G lying closer to u than to v and nev(e|G) is the number of edges of G lying closer to v than to u. An efficient formula for… (More)

- Shubo Chen, Weijun Liu
- 2012

For a graph G = (V,E), the modified Schultz index of G is defined as S∗(G) = ∑ {u,v}⊆V (G) (dG(u) · dG(v))dG(u, v) where dG(u) (or d(u)) is the degree of the vertex u of G, and dG(u, v) is the distance between u and v. Let B(n) be the set of bicyclic graph with n vertices. In this paper, we study the modified Schultz index of B(n), graphs in B(n) with the… (More)

- Shubo Chen, Weijun Liu
- Graphs and Combinatorics
- 2014

For a graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Denote by Gn,k the set of graphs with n vertices and k cut edges. In this paper, we showed the types of graphs with the largest and the… (More)

If G is a (molecular) graph with n vertices, and di is the degree of its i-th vertex, then the sum-connectivity index of G is the sum of the weights (du +dv)− 1 2 of all edges uv of G. A polyomino system is a finite 2-connected plane graph such that each interior face (or say a cell) is surrounded by a regular square of length one. Formulas for calculating… (More)

The Randić index R(G) of an organic molecule whose molecular graph is G is the sum of the weights (dudv)− 1 2 of all edges uv of G, where du(or dv) denote the degree of vertex u(or v). Efficient formulas for calculating the Randić index of polyomino chains are provided. Mathematics Subject Classification: 05C50, 05C12, 05C05

- Liwen Xiao, Shubo Chen, Zhijun Guo, Qiao Chen
- 2010

The geometric-arithmetic index of graph G is defined as GA(G) = ∑ uv∈E(G) 2 √ dudv du+dv , du (or dv) is the degree the vertex u (or v). The GA index of benzenoid systems and phenylenes are computed, a simple relation is established between the geometric-arithmetic of a phenylene and the corresponding hexagonal squeeze in this paper. Mathematics Subject… (More)

- Shubo Chen, Kejing He
- SmartCity
- 2015

This paper mainly deals with the detection problem of the target with low Radar Cross-Section (RCS) in heavy sea clutter with unknown Power Spectral Density (PSD). Since the performance of traditional single-scan detectors degrades as the target of interest is smaller and weaker, three adaptive detectors, based upon a two-step design procedure, are proposed… (More)

- Shubo Chen
- J. Comb. Optim.
- 2016