Steiner 3-diameter, maximum degree and size of a graph. Issue 2 (3rd April 2022)

• Record Type: Journal Article
• Authors: Mao, Yaping
• Is Part Of: International journal of computer mathematics. Volume 7:Issue 2(2022)
• Page Start: 95
• Page End: 111
• Publication Date: 2022-04-03
• Subjects: Diameter -- Steiner diameter -- maximum degree; 05C05 -- 05C12 -- 05C35; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2022.2039963
• Languages: English
• ISSNs: 2379-9927

Abstract

Abstract : The Steiner k -diameter sdiam k ⁡ ( G ) of a graph G, introduced by Chartrand, Oellermann, Tian and Zou in 1989, is a natural generalization of the concept of classical diameter. When k = 2, sdiam 2 ⁡ ( G ) = diam ( G ) is the classical diameter. The problem of determining the minimum size of a graph of order n whose diameter is at most d and whose maximum degree is ℓ was first introduced by Erdös and Rényi. In this paper, we generalize the above problem for Steiner k -diameter, and study the problem of determining the minimum size of a graph of order n whose Steiner 3-diameter is at most d and whose maximum degree is at most ℓ.