A sufficient condition for r - graphic sequences to be potentially. (2nd January 2019)

• Record Type: Journal Article
• Authors: Chat, Bilal A.; Samee, U.; Pirzada, S.
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 22:Number 1(2019)
• Page Start: 1
• Page End: 8
• Publication Date: 2019-01-02
• Subjects: 05C07 -- 05C35; r-graph -- r-split graph -- r-graphic sequence; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2018.1555079
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: An r -graph is a multigraph in which two vertices are joined by at most r edges. An r -complete graph on n vertices, denoted by, is an r -graph on n vertices in which each pair of vertices is joined by exactly r -edges. The r -split graph on l+m vertices is denoted by . A non increasing sequence p = ( d, d, … , d) of non negative integers is said to be r -graphic if it is realizable by an r-graph on n vertices. An r -graphic sequence π is said to be potentially -graphic if it has a realization containing as a subgraph. In this paper, we obtain conditions for r -graphic sequences to be potentially and give a Rao-type characterizations for π to be potentially -graphic.