Shubo Chen

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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)
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)
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)
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)