University of Isfahan Transactions on Combinatorics 2251-8657 4 4 2015 12 01 The resistance distance and the Kirchhoff index of the $k$-th semi total point graphs 33 41 7767 10.22108/toc.2015.7767 EN Denglan Cui Department of Mathematics Hunan Nornal University Changsha, Hunan 410081 Yaoping Hou Department of Mathematics Hunan Normal University Changsha, Hunan,410081 Journal Article 2014 12 16 ‎The $k$-th semi-total point graph $R^k(G)$ of a graph $G$‎, ‎is a graph obtained from $G$ by adding $k$ vertices corresponding to each edge and connecting them to the endpoints of the edge considered‎. ‎In this paper‎, ‎we obtain formulas for the resistance distance and Kirchhoff index of $R^k(G).$‎   https://toc.ui.ac.ir/article_7767_d003df08d9fc1d3ea3e0f98ad110cc1b.pdf