Abstract
A graph is said to be embedded in the plane if it can be drawn on the plane so that no two edges intersect. Such a graph is called a planar graph. Graphs arising from maps are clearly planar. In fact, planar maps can be characterized as such. Any planar map cuts out the plane into faces. To be precise, a maximal region of the plane which does not contain in its interior a vertex of the graph is called a face. A finite plane graph has also one unbounded face called the outer face. The faces are pairwise disjoint. The basic relation for planar graphs is the following theorem due to Euler.
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© 2009 Hindustan Book Agency
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Cioabă, S.M., Murty, M.R. (2009). Planar Graphs. In: A First Course in Graph Theory and Combinatorics. Texts and Readings in Mathematics, vol 55. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-39-2_10
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DOI: https://doi.org/10.1007/978-93-86279-39-2_10
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-98-2
Online ISBN: 978-93-86279-39-2
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