The Number of Blocks of a Graph with Given Minimum Degree. (25th January 2021)

• Record Type: Journal Article
• Authors: Li, Lei; Wu, Baoyindureng
• Other Names: Matouk A. E. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2021(2021)
• Publication Date: 2021-01-25
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2021/6691960
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : A block of a graph is a nonseparable maximal subgraph of the graph. We denote by b G the number of block of a graph G . We show that, for a connected graph G of order n with minimum degree k ≥ 1, b G < 2 k − 3 / k 2 − k − 1 n . The bound is asymptotically tight. In addition, for a connected cubic graph G of order n ≥ 14, b G ≤ n / 2 − 2 . The bound is tight.