Resistance characterizations of equiarboreal graphs |
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Authors: | Jiang Zhou Lizhu Sun Changjiang Bu |
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Institution: | 1. College of Science, Harbin Engineering University, Harbin 150001, PR China;2. Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong |
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Abstract: | A weighted (unweighted) graph is called equiarboreal if the sum of weights (the number) of spanning trees containing a given edge in is independent of the choice of edge. In this paper, we give some resistance characterizations of equiarboreal weighted and unweighted graphs, and obtain the necessary and sufficient conditions for -subdivision graphs, iterated double graphs, line graphs of regular graphs and duals of planar graphs to be equiarboreal. Applying these results, we obtain new infinite families of equiarboreal graphs, including iterated double graphs of 1-walk-regular graphs, line graphs of triangle-free 2-walk-regular graphs, and duals of equiarboreal planar graphs. |
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Keywords: | Spanning tree Equiarboreal graph Laplacian matrix Resistance distance |
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