Two-Point Resistances in Sailboat Fractal Networks

Abstract

The two-point resistance of fractal network has been studied extensively by mathematicians and physicists. In this paper, for a class of self-similar networks named sailboat networks, we obtain a recursive algorithm for computing resistance between any two nodes, using elimination principle, substitution principle and local sum rules on effective resistance.

A Novel and Efficient Method for Computing the Resistance Distance

“…There are numbers of techniques and formulae have been developed for calculating the resistance distance, i.e., algebraic formulae [17], [19]- [24], series and parallel rules, combinatorial formula [4], deltawye transformation [16], sum rules [17], [18], star-triangle transformation [16], probabilistic formulae [4], [25], starmesh transformation, the principle of elimination, recursion formula [26], the principle of substitution and so forth. By using above methods and formulas, resistance distance in many networks and graphs has been discussed before, i.e., Potting network [40], circulant graphs [27], Sailboat fractal networks [39], Cayley graphs [28], complete n-partite graphs [29], wheels and fans [30], Double graphs; graph with an involution [31], regular graphs [32], [33], pseudodistance-regular graphs [34], distance-regular graphs [50], some fullerene graphs [35], Sierpinski gasket network [36], ring-type network [37], maximum and minimum resistance distance in n-dimensional hypercubes [38], and others [41]- [47]. But, it is not easy to get the resistance distance in complex networks.…”