Resistance matrix and q-Laplacian of a unicyclic graph
نویسنده
چکیده
The resistance distance between two vertices of a graph can be defined as the effective resistance between the two vertices, when the graph is viewed as an electrical network with each edge carrying unit resistance. The concept has several different motivations. The resistance matrix of a graph is a matrix with its (i, j)-entry being the resistance distance between vertices i and j. We obtain an explicit formula for the determinant of the resistance matrix of a unicyclic graph. Some properties of a q-analogue of the Laplacian are also studied, with special attention to the limiting behaviour as q approaches 1. An expression for the inverse of the q-Laplacian of a unicyclic graph is derived.
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