Bicyclic graphs with maximal edge revised Szeged index
Bicyclic graphs with maximal edge revised Szeged index
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DOI：
10.1016/j.dam.2016.07.005
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发表时间：
2016-12
期刊：
影响因子：
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通讯作者：
Mengmeng Liu;Lily Chen
中科院分区：
文献类型：
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作者：
Mengmeng Liu;Lily Chen
定义边修正Szeged指数Szeged（G）=∑ e= uv ∈ E（mu（e）+m0（e）/2）（mv（e）+m0（e）/2），其中mu（e）和mv（e）分别是G中离顶点u比离顶点v近的边数和离顶点v比离顶点u近的边数，m 0（e）是与u和v等距的边数.本文给出了m≥ 5的连通双圈图的边修正Szeged指数的一个上界，即Szeged指数（G）≤{（m 3− 4 m+ 16）/4，如果m是奇数，（m 3− 4 m+ 18）/4，如果m是偶数且相等当且仅当G是从圈Cm − 2复制一个顶点得到的图。
The edge revised Szeged index S z e∗(G) is defined as S z e∗(G)=∑ e= u v∈ E (m u (e)+ m 0 (e)/2)(m v (e)+ m 0 (e)/2), where m u (e) and m v (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 m 0 (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 m≥ 5, that is, S z e∗(G)≤{(m 3− 4 m+ 16)/4, if m is odd,(m 3− 4 m+ 18)/4, if m is even with equality if and only if G is the graph obtained from the cycle C m− 2 by duplicating a single vertex.