On the further relation between the (revised) Szeged index and the Wiener index of graphs
نویسندگان
چکیده
منابع مشابه
On the revised edge-Szeged index of graphs
The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of ed...
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Let Sz(G) and W (G) be the revised Szeged index and the Wiener index of a graph G. Chen, Li, and Liu [European J. Combin. 36 (2014) 237–246] proved that if G is a non-bipartite connected graph of order n ≥ 4, then Sz(G) −W (G) ≥ ( n + 4n− 6 ) /4. Using a matrix method we prove that if G is a non-bipartite graph of order n, size m, and girth g, then Sz(G)−W (G) ≥ n ( m− 3n 4 ) + P (g), where P i...
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Let W (G) and Sz(G) be the Wiener index and the Szeged index of a connected graph G. It is proved that if G is a connected bipartite graph of order n ≥ 4, size m ≥ n, and if ` is the length of a longest isometric cycle of G, then Sz(G) − W (G) ≥ n(m − n + ` − 2) + (`/2) − ` + 2`. It is also proved if G is a connected graph of order n ≥ 5 and girth g ≥ 5, then Sz(G) − W (G) ≥ PIv(G) − n(n − 1) +...
متن کاملOn the difference between the Szeged and the Wiener index
We prove a conjecture of Nadjafi-Arani et al. on the difference between the Szeged and the Wiener index of a graph (M. J. Nadjafi-Arani, H. Khodashenas, A. R. Ashrafi: Graphs whose Szeged and Wiener numbers differ by 4 and 5, Math. Comput. Modelling 55 (2012), 1644–1648). Namely, if G is a 2-connected non-complete graph on n vertices, then Sz (G) −W (G) ≥ 2n − 6. Furthermore, the equality is ob...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.01.029