The Laplacian polynomial and Kirchhoff index of graphs derived from regular graphs.

Abstract: Let be the graph obtained from by adding a new vertex corresponding to each edge of and by joining each new vertex to the end vertices of the corresponding edge, and be the graph obtained from by inserting a new vertex into every edge of and by joining by edges those pairs of these new vertices which lie on adjacent edges of . In this paper, we determine the Laplacian polynomials of and of a regular graph ; on the other hand, we derive formulae and lower bounds of the Kirchhoff index of these graphs. [Copyright &y& Elsevier]