- Volume 39 Issue 1
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.
- Bull. Korean Math. Soc. v.37 Line graphs of covering gpaphs are cover graphs D. Archdeacon;J. Lee;M. Y. Sohn
- Topological graph Theory J. L. Gross;T. W. Tucker
- Discrete Math. v.18 Generating all graphs by permutation voltage assignments https://doi.org/10.1016/0012-365X(77)90131-5
- Rend. Circ. Math. Palermo v.9 Some properties of line digraphs F. Harary;R. Z. Norman https://doi.org/10.1007/BF02854581
- J. graph Theory v.2 Generalized embedding schemes S. Stahl https://doi.org/10.1002/jgt.3190020106
- Amer. J. Math. v.55 2-isomorphic graphs H. Whitney https://doi.org/10.2307/2371127