CELLULAR EMBEDDINGS OF LINE GRAPHS AND LIFTS

Abstract

A Cellular embedding of a graph G into an orientable surface S can be considered as a cellular decomposition of S into 0-cells, 1-cells and 2-cells and vise versa, in which 0-cells and 1-cells form a graph G and this decomposition of S is called a map in S with underlying graph G. For a map M with underlying graph G, we define a natural rotation on the line graph of the graph G and we introduce the line map for M. we find that genus of the supporting surface of the line map for a map and we give a characterization for the line map to be embedded in the sphere. Moreover we show that the line map for any life of a map M is map-isomorphic to a lift of the line map for M.

Keywords

• graph;
• cellular embedding;
• permutation voltage assignment;
• lift rotation;
• map;
• graph-isomorphism;
• map-isomorphism;
• line graph;
• line map

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References

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