On the g-good-neighbor connectivity of graphs

Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network G. In 1996, Fabrega and Fiol proposed the g-good-neighbor connectivity of G. In this paper, we show that 1 <= kappa(g)(G) <= n - 2g - 2 for 0 <= g <= {Delta(G), left perpendicular n-3/2 right perpendicular}, and graphs with kappa(g)(G) = 1, 2 and trees with kappa(g)(T-n) = n - t for 4 <= t <= n+2/2 are characterized, respectively. In the end, we get the three extremal results for the g-good-neighbor connectivity. (C) 2019 Elsevier B.V. All rights reserved.