An Algorithm for One-to-One Mapping Matrix-star Graph into Transposition Graph

Abstract

The matrix-star and the transposition graphs are considered as star graph variants that have various merits in graph theory such as node symmetry, fault tolerance, recursive scalability, etc. This paper describes an one-to-one mapping algorithm from a matrix-star graph to a transposition graph using adjacent properties in graph theory. The result show that a matrix-star graph MS 2,n can be embedded in a transposition graph T 2n with dilation n or less and average dilation 2 or less.