International Journal of Nonlinear Analysis and Applications

A classification of total irregularity of polyomino chains based on segments by using non-decreasing real function

Articles in Press

Document Type : Research Paper

Author

Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran

Abstract

The total irregularity is a type of graph invariant and for a given simple graph $ G$ is calculated by the formula, $irr_t(G)=\dfrac{1}{2}\sum_{\{u,v\} \subseteq V(G)}\mid deg_Gu-deg_Gv\mid$, in which $deg_Gv$ is the degree of the vertex $v$ of $G$. This paper aims to offer a classification of polyomino chains based on segments in terms of total irregularity. We can find a sequence for all polyomino chains concerning this graph invariant by defining a non-decreasing function.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 21 February 2025
  • Receive Date: 27 December 2022
  • Accept Date: 27 January 2023