Extremal algebraic connectivities of certain caterpillar classes and symmetric caterpillars

Oscar Rojo, Luis Medina, Nair M.M. de Abreu, Claudia Justel
2010 The Electronic Journal of Linear Algebra  
A caterpillar is a tree in which the removal of all pendant vertices makes it a path. Let d ≥ 3 and n ≥ 6 be given. Let P d−1 be the path of d − 1 vertices and Sp be the star of p + 1 vertices. Let p = [p 1 , p 2 , ..., p d−1 ] such that p 1 ≥ 1, p 2 ≥ 1, ..., p d−1 ≥ 1. Let C (p) be the caterpillar obtained from the stars Sp 1 , Sp 2 , ..., Sp d−1 and the path P d−1 by identifying the root of Sp i with the i−vertex of P d−1 . Let n > 2 (d − 1) be given. Let In this paper, the caterpillars in C
more » ... and in S having the maximum and the minimum algebraic connectivity are found. Moreover, the algebraic connectivity of a caterpillar in S as the smallest eigenvalue of a 2 × 2 -block tridiagonal matrix of order 2s × 2s if d = 2s + 1 or d = 2s + 2 is characterized.
doi:10.13001/1081-3810.1364 fatcat:ocmn7kjtfba23fwqe4vg3bvxfy