Theoretical and Computational Methods to Resistance Distances in Novel Graphs Operations
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">$G_{1}(\vee _{H})G_{2}$ </t...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2019-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8786256/ |
| _version_ | 1811212429847166976 |
|---|---|
| author | Li Zhang Jia-Bao Liu |
| author_facet | Li Zhang Jia-Bao Liu |
| author_sort | Li Zhang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T05:29:16Z |
| format | Article |
| id | doaj.art-c7531e8563d94218bad61ec11abbfcbb |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-12T05:29:16Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-c7531e8563d94218bad61ec11abbfcbb2022-12-22T03:46:10ZengIEEEIEEE Access2169-35362019-01-01710790810791610.1109/ACCESS.2019.29327718786256Theoretical and Computational Methods to Resistance Distances in Novel Graphs OperationsLi Zhang0Jia-Bao Liu1https://orcid.org/0000-0002-9620-7692School of Mathematics and Physics, Anhui Jianzhu University, Hefei, ChinaSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei, ChinaMotivated 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.https://ieeexplore.ieee.org/document/8786256/Graphresistance distanceLaplacian matrix{1}-inversegroup inverse |
| spellingShingle | Li Zhang Jia-Bao Liu Theoretical and Computational Methods to Resistance Distances in Novel Graphs Operations IEEE Access Graph resistance distance Laplacian matrix {1}-inverse group inverse |
| title | Theoretical and Computational Methods to Resistance Distances in Novel Graphs Operations |
| title_full | Theoretical and Computational Methods to Resistance Distances in Novel Graphs Operations |
| title_fullStr | Theoretical and Computational Methods to Resistance Distances in Novel Graphs Operations |
| title_full_unstemmed | Theoretical and Computational Methods to Resistance Distances in Novel Graphs Operations |
| title_short | Theoretical and Computational Methods to Resistance Distances in Novel Graphs Operations |
| title_sort | theoretical and computational methods to resistance distances in novel graphs operations |
| topic | Graph resistance distance Laplacian matrix {1}-inverse group inverse |
| url | https://ieeexplore.ieee.org/document/8786256/ |
| work_keys_str_mv | AT lizhang theoreticalandcomputationalmethodstoresistancedistancesinnovelgraphsoperations AT jiabaoliu theoreticalandcomputationalmethodstoresistancedistancesinnovelgraphsoperations |