Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949931 | Discrete Applied Mathematics | 2016 | 6 Pages |
Abstract
The edge revised Szeged index Szeâ(G) is defined as Szeâ(G)=âe=uvâE(mu(e)+m0(e)/2)(mv(e)+m0(e)/2), where mu(e) and mv(e) are, respectively, the number of edges of G lying closer to vertex u than to vertex v and the number of edges of G lying closer to vertex v than to vertex u, and m0(e) is the number of edges equidistant to u and v. In this paper, we give an upper bound of the edge revised Szeged index for a connected bicyclic graphs with size mâ¥5, that is, Szeâ(G)â¤{(m3â4m+16)/4,if m  is odd ,(m3â4m+18)/4,if m  is even with equality if and only if G is the graph obtained from the cycle Cmâ2 by duplicating a single vertex.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Mengmeng Liu, Lily Chen,