Archimedean tiling graphs with Gallai’s property

Abstract

Gallai in 1966 raised the question about the existence of graphs with the property that every vertex is missed by some longest path. This property will be called Gallai’s property. In this paper we present some graphs embeddable into Archimedean tiling graphs, with both connectivity 1 and 2, satisfying Gallai’s property.

Keywords

• gallai’s property
• archimedean tiling graphs
• the longest path
• primary 05c38
• secondary 05c62