AbstractIn this paper, the planar polynomial of a graph is introduced and some of its properties are discussed. The planar polynomial of the graph G is real-rooted if and only if G is planar. This polynomial is not EE-invariant. Some useful results about the roots of planar polynomial of complete graphs are presented. Moreover, all the graphs whose planar polynomial is of degree five are characterized.
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Tolue et al. (2024) studied this question.
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