On the extension of connected irregular (λ, μ)-graphs. (3rd April 2017)

• Record Type: Journal Article
• Authors: Hailat, Mohammad
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 20:Number 3(2017)
• Page Start: 663
• Page End: 671
• Publication Date: 2017-04-03
• Subjects: (λ, μ)-graph -- Strongly regular graphs; 05C75; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2016.1140869
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: Let λ and μ be any nonnegative integers. A graph G is called a ( λ, μ )-graph if every pair of adjacent vertices have λ common neighbors, and every pair of non-adjacent vertices have μ common neighbors. Thus, ( λ, μ )-graphs are generalization of strongly regular graphs obtained by lessening the regularity property on vertex degrees. In this paper, we will show that a ( λ, 1)-graph, with n vertices, is of type K 1 ∨ ( s 2 K 2 ∪ s 3 K 3 ∪ … ∪ st Kt ) such that si ≥ 0, for all i = 1, … , t and 1 + 2 s 2 + … + ts t = n . Note that λ can take several values in the same graph.