The reformulated Zagreb indices of tricyclic graphs

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• 作者：Shengjin Ji ; ^a ; ^{jishengjin2013@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yongke Qu^b ; ^{yongke1239@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xia Li^a ; ^{summer08lixia@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：The reformulated Zagreb index ; Zagreb indices ; Tricyclic graph ; Degree of edge ; Graph operation
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：1 October 2015
• 年：2015
• 卷：268
• 期：Complete
• 页码：590-595
• 全文大小：637 K

文摘

Mili$\stackrel{藰}{c}$evi$\acute{c}$ et al. first introduced the reformulated Zagreb indices, which is a generalization of classical Zagreb indices of chemical graph theory. As we know, the Zagreb indices have been found applications in QSPR and QSAR studies. In the paper, we characterize the extremal properties of the first reformulated Zagreb index. We show some graph operations which increase or decrease this index. Furthermore, we determine the sharp bound of the first reformulated Zagreb index among all the extremal tricyclic graphs by these graph operations.