On Weighted PI Index of Graphs

详细信息    查看全文

• 作者：K. Pattabiraman ^{pramank@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; P. Kandan ^{kandan2k@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Generalized hierarchical product ; Cartesian product ; join ; vertex PI index ; weighted PI index
• 刊名：Electronic Notes in Discrete Mathematics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：53
• 期：Complete
• 页码：225-238
• 全文大小：271 K

文摘

The vertex PI index of a graph G  , denoted by PI_v(G)$P{I}_v(G)$, is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. Similarly, the Weighted PI index of a graph G  , denoted by $P{I}_w(G)={\sum }_{uv=e\in E(G)}(d_G(u)+d_G(v))(n_u^G(e)+n_v^G(e))$, where d_G(u)$d_G(u)$ is the degree of the vertex u in G  . In this paper, the exact formula for the weighted PI indices of generalized hierarchical product and join of two graphs are obtained. Using the result obtained here, some known result is deduced as corollary. Also, we obtain the weighted PI indices of the zig-zag polyhex nanotube TUHC₆[2n,2]$TUH{C}_6[2n,2]$, hexagonal chain L_n$L_n$, the molecular graph of Truncated Cube, fan and wheel graphs.