The Irregularity Polynomials of Fibonacci and Lucas cubes

Irregularity of a graph is an invariant measuring how much the graph differs from a regular graph. Albertson index is one measure of irregularity, defined as the sum of | d e g ( u ) - d e g ( v ) | over all edges uv of the graph. Motivated by a recent result on the irregularity of Fibonacci cubes,...

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Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 44; no. 2; pp. 753 - 765
Main Authors Eğecioğlu, Ömer, Saygı, Elif, Saygı, Zülfükar
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.03.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Cubes
Graph theory
Hypercubes
Irregularities
Mathematics
Mathematics and Statistics
Polynomials
Topology
05C31
11B39
Irregularity of graph
Fibonacci cube
Lucas cube
05C35
05A15
Online AccessGet full text
ISSN0126-6705
2180-4206
DOI10.1007/s40840-020-00981-0

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Summary:Irregularity of a graph is an invariant measuring how much the graph differs from a regular graph. Albertson index is one measure of irregularity, defined as the sum of | d e g ( u ) - d e g ( v ) | over all edges uv of the graph. Motivated by a recent result on the irregularity of Fibonacci cubes, we consider irregularity polynomials and determine them for Fibonacci and Lucas cubes. These are graph families that have been studied as alternatives for the classical hypercube topology for interconnection networks. The irregularity polynomials specialize to the Albertson index and also provide additional information about the higher moments of | d e g ( u ) - d e g ( v ) | in these families of graphs.
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ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-020-00981-0