On Ramsey (P3, C6)-minimal graphs for certain order. (May 2020)

• Record Type: Journal Article
• Authors: Nisa, F; Rahmadani, D; Purwanto, ; Susanto, H
• Is Part Of: Journal of physics. Volume 1538(2020)
• Publication Date: 2020-05
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1538/1/012011
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: Let F, G and H be graphs. Notation F → ( G, H ) means that there is any two-coloring, say red and blue, of all edges of F which contains red subgraph isomorphic to G or blue subgraph isomorphic to H. The graph F is Ramsey ( G, H )-minimal graph if F → ( G, H ) but F − e ↛ ( G, H ) for any e ∈ E ( F ). The class of all Ramsey ( G, H )-minimal graphs will be denoted by R ( G, H ). In this paper, we proved that there are only two graphs with six vertices that belong to Ramsey minimal graphs for certain pair of path and cycle ( P 3, C 6 ) and we also determined some graphs with eight vertices in R ( P 3, C 6 ).