Resistance Distances in Linear Polyacene Graphs

Abstract

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The resistance distance between any two vertices of a connected graph is defined as the net effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. In this article, using electric network approach and combinatorial approach, we derive exact expression for resistance distances between any two vertices of polyacene graphs.

Keywords

• hexagonal lattice
• local rules
• polyacene graph
• resistance distance
• circuit reduction