Cacti with minimum, second-minimum, and third-minimum Kirchhoff indices
نویسندگان
چکیده
Resistance distance was introduced by Klein and Randić. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all pairs of vertices. A graph G is called a cactus if each block of G is either an edge or a cycle. Denote by Cat(n; t) the set of connected cacti possessing n vertices and t cycles. In this paper, we give the first three smallest Kirchhoff indices among graphs in Cat(n; t), and characterize the corresponding extremal graphs as well. AMS subject classifications: 05C12, 05C90
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