Planarity in vague graphs with application

Ghorai, Ganesh and Pal, Madhumangal (2017) Planarity in vague graphs with application. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 33 (2). pp. 147-164. ISSN 0866-0174

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Abstract

In lots of practical applications with a graph structure, there may exist crossing between edges. Crossing between edges is not allowed in crisp planar graph. Crossing of edges can be considered in a vague multigraph with certain amount of vague planarity value. This is why the notion of vague multiset is introduced. Then vague multigraphs, vague planar graphs, vague strong edges, vague faces, strong vague faces are defined. The vague dual graph of a vague planar graph is also introduced. Several properties of vague planar graphs and vague dual graphs are also studied. An application of vague planar graph is also given.

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