Find in Library

Motivated by the recent research on the computation of resistance distance, this paper aims to compute resistance distance in two classes of graphs, which are generated by three graphs. In fact, they are <inline-formula> <tex-math notation="LaTeX">$G_{1}(\vee _{H})G_{2}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$G_{0}^{S}\lhd (G_{1}^{V}\cup G_{2}^{E})$ </tex-math></inline-formula>. In this paper, we first give the <inline-formula> <tex-math notation="LaTeX">$\{1\}$ </tex-math></inline-formula>-inverses of the Laplacian matrix of <inline-formula> <tex-math notation="LaTeX">$G_{1}(\vee _{H})G_{2}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$G_{0}^{S}\lhd (G_{1}^{V}\cup G_{2}^{E})$ </tex-math></inline-formula> by calculation. Then connected with the relationship between resistance distance and the <inline-formula> <tex-math notation="LaTeX">$\{1\}$ </tex-math></inline-formula>-inverses of the Laplacian matrices, we would obtain resistance distance in <inline-formula> <tex-math notation="LaTeX">$G_{1}(\vee _{H})G_{2}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$G_{0}^{S}\lhd (G_{1}^{V}\cup G_{2}^{E})$ </tex-math></inline-formula>. In addition, we finally list two examples to illustrate the efficiency of our proposed method.