Croatica Chemica Acta, Vol. 87 No. 1, 2014.
Original scientific paper
https://doi.org/10.5562/cca2318
Relations Between Resistance Distances of a Graph and its Complement or its Contraction
Yujun Yang
; School of Mathematics and Information Science, Yantai University, Yantai, Shandong, 264005, P.R. China. Mathematical chemistry group, Texas A&M University at Galveston, Galveston, Texas, 77553-1675, USA School of Mathematics, Shandong University, Jinan, S
Abstract
The resistance distance between two vertices of a connected graph is defined as the net effective resistance between them when each edge of the graph is replaced by a resistor. In this paper, it is shown that the product of resistance distances between any pair of vertices in a simple graph and in its connected complement is less than or equal to 3. Meanwhile, a relation between resistance distances of a graph and its contraction is obtained in a special case. (doi: 10.5562/cca2318)
Keywords
resistance distance; graph complement; graph contraction; Rayleigh's short-cut principle
Hrčak ID:
122280
URI
Publication date:
30.4.2014.
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