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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Bibliographic Details
Main Author: Lubguban, Alona A.
Format: text
Language:English
Published: Animo Repository 2014
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Online Access:https://animorepository.dlsu.edu.ph/etd_doctoral/394
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Institution: De La Salle University
Language: English
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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.