Minimal Embedding of Hypercubic Graphs on Surface

Abstract

In this paper, we propose a minimal embedding of a non-planar, n-dimensional hypercubic graph on a surface as a “standard” embedding. The “standard” form of embedding graph on a surface has been understudied and therefore, has remained undefined. The aim of this paper is to define what the “standard form” is for a non-planar graph, while distinguishing different embedding patterns of a graph. As a result, we defined a value ω(G) for all non-planar graphs G, and determined the value ω(Q _n ) for n-dimensional hypercubic graphs denoted by Q _n .