Resistance distance in some composition of graphs
In graph theory, the resistance distance between any two vertices of a simple connected graph G is equal to the e ective resistance between two corresponding nodes on an electrical network, constructed so as to correspond to G, with each edge being replaced by a unit resistor or a 1 ohm resistance....
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Format: | text |
Language: | English |
Published: |
Animo Repository
2014
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Subjects: | |
Online Access: | https://animorepository.dlsu.edu.ph/etd_doctoral/394 |
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Institution: | De La Salle University |
Language: | English |
Summary: | In graph theory, the resistance distance between any two vertices of a simple connected graph G is equal to the e ective resistance between two corresponding nodes on an electrical network, constructed so as to correspond to G, with each edge being replaced by a unit resistor or a 1 ohm resistance. This resistance is known to be a metric on a graph.
This paper aims to nd an explicit expression for the resistance distance between any pair of vertices in some composition of graphs. Speci cally, the e ective resis- tance between any two vertices in each graph of Pn[Km] Tn[Km] Cn[Km] Pn[Km] Tn[Km] Cn[Km] are determined.
The relationship between the resistance distance between two vertices in a graph and its complement will be investigated. |
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