Further Results on Resistance Distance and Kirchhoff Index in Electric Networks
In electric circuit theory, it is of great interest to compute the effective resistance between any pairs of vertices of a network, as well as the Kirchhoff index. Let Q(G) be the graph obtained from G by inserting a new vertex into every edge of G and by joining by edges those pairs of these new ve...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/4682527 |
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| author | Qun Liu Jia-Bao Liu Jinde Cao |
| author_facet | Qun Liu Jia-Bao Liu Jinde Cao |
| author_sort | Qun Liu |
| collection | DOAJ |
| description | In electric circuit theory, it is of great interest to compute the effective resistance between any pairs of vertices of a network, as well as the Kirchhoff index. Let Q(G) be the graph obtained from G by inserting a new vertex into every edge of G and by joining by edges those pairs of these new vertices which lie on adjacent edges of G. The set of such new vertices is denoted by I(G). The Q-vertex corona of G1 and G2, denoted by G1⊙QG2, is the graph obtained from vertex disjoint Q(G1) and VG1 copies of G2 by joining the ith vertex of V(G1) to every vertex in the ith copy of G2. The Q-edge corona of G1 and G2, denoted by G1⊖QG2, is the graph obtained from vertex disjoint Q(G1) and IG1 copies of G2 by joining the ith vertex of I(G1) to every vertex in the ith copy of G2. The objective of the present work is to obtain the resistance distance and Kirchhoff index for composite networks such as Q-vertex corona and Q-edge corona networks. |
| format | Article |
| id | doaj-art-ac80b73f292d47c48d2aae6349f95a37 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-ac80b73f292d47c48d2aae6349f95a372025-02-03T06:07:11ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/46825274682527Further Results on Resistance Distance and Kirchhoff Index in Electric NetworksQun Liu0Jia-Bao Liu1Jinde Cao2Department of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, ChinaDepartment of Public Courses, Anhui Xinhua University, Hefei 230088, ChinaResearch Center for Complex Systems and Network Science, Department of Mathematics, Southeast University, Nanjing 210096, ChinaIn electric circuit theory, it is of great interest to compute the effective resistance between any pairs of vertices of a network, as well as the Kirchhoff index. Let Q(G) be the graph obtained from G by inserting a new vertex into every edge of G and by joining by edges those pairs of these new vertices which lie on adjacent edges of G. The set of such new vertices is denoted by I(G). The Q-vertex corona of G1 and G2, denoted by G1⊙QG2, is the graph obtained from vertex disjoint Q(G1) and VG1 copies of G2 by joining the ith vertex of V(G1) to every vertex in the ith copy of G2. The Q-edge corona of G1 and G2, denoted by G1⊖QG2, is the graph obtained from vertex disjoint Q(G1) and IG1 copies of G2 by joining the ith vertex of I(G1) to every vertex in the ith copy of G2. The objective of the present work is to obtain the resistance distance and Kirchhoff index for composite networks such as Q-vertex corona and Q-edge corona networks.http://dx.doi.org/10.1155/2016/4682527 |
| spellingShingle | Qun Liu Jia-Bao Liu Jinde Cao Further Results on Resistance Distance and Kirchhoff Index in Electric Networks Discrete Dynamics in Nature and Society |
| title | Further Results on Resistance Distance and Kirchhoff Index in Electric Networks |
| title_full | Further Results on Resistance Distance and Kirchhoff Index in Electric Networks |
| title_fullStr | Further Results on Resistance Distance and Kirchhoff Index in Electric Networks |
| title_full_unstemmed | Further Results on Resistance Distance and Kirchhoff Index in Electric Networks |
| title_short | Further Results on Resistance Distance and Kirchhoff Index in Electric Networks |
| title_sort | further results on resistance distance and kirchhoff index in electric networks |
| url | http://dx.doi.org/10.1155/2016/4682527 |
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