Research Article

Planar polynomial of the graphs

Published in: Quaestiones Mathematicae
Volume 47 , issue 6 , 2024 , pages: 1239–1256

DOI: 10.2989/16073606.2024.2320434

Author(s): Behnaz Tolue Hakim Sabzevari University, Iran , Alireza Doostabadi University of Zabol, Iran , Sayed Masih Ayat University of Zabol, Iran

Keywords: 05C31 , 05C10 , 05C30 , Induced planar subgraphs , planar polynomial , polynomial degree

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Abstract

In 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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