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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Abstract 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.
AbstractList 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 |deg(u)-deg(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 |deg(u)-deg(v)| in these families of graphs.
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.
Author Eğecioğlu, Ömer
Saygı, Elif
Saygı, Zülfükar
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crossref_primary_10_1016_j_tcs_2021_04_019
crossref_primary_10_1016_j_disc_2023_113851
crossref_primary_10_1016_j_dam_2021_05_018
Cites_doi 10.1109/71.205649
10.1016/j.dam.2018.05.013
10.1007/s40840-020-00932-9
10.1002/jgt.3190110214
10.1080/07468342.1988.11973088
10.1007/s10878-011-9433-z
10.1016/j.dam.2018.05.015
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Keywords 05C31
11B39
Irregularity of graph
Fibonacci cube
Lucas cube
05C35
05A15
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References Hsu (CR6) 1993; 4
Alavi, Chartrand, Chung, Erdős, Graham, Oellermann (CR2) 1987; 11
Albertson (CR3) 1997; 46
Saygı, Eğecioğlu (CR10) 2019; 266
Réti (CR9) 2019; 344–345
Chartrand, Erdős, Oellermann (CR5) 1988; 19
Abdo, Dimitrov, Gutman (CR1) 2018; 250
Alizadeh, Deutsch, Klavžar (CR4) 2020
Klavžar (CR7) 2013; 25
Munarini, Cippo, Zagaglia Salvi (CR8) 2001; 39
MO Albertson (981_CR3) 1997; 46
W-J Hsu (981_CR6) 1993; 4
E Saygı (981_CR10) 2019; 266
S Klavžar (981_CR7) 2013; 25
H Abdo (981_CR1) 2018; 250
Y Alizadeh (981_CR4) 2020
E Munarini (981_CR8) 2001; 39
Y Alavi (981_CR2) 1987; 11
T Réti (981_CR9) 2019; 344–345
G Chartrand (981_CR5) 1988; 19
References_xml – volume: 4
  start-page: 3
  year: 1993
  end-page: 12
  ident: CR6
  article-title: Fibonacci cubes-a new interconnection technology
  publication-title: IEEE Trans. Parallel Distrib. Syst.
  doi: 10.1109/71.205649
– volume: 46
  start-page: 219
  year: 1997
  end-page: 225
  ident: CR3
  article-title: The irregularity of a graph
  publication-title: Ars Combin.
– volume: 250
  start-page: 57
  year: 2018
  end-page: 64
  ident: CR1
  article-title: Graphs with maximal irregularity
  publication-title: Discrete Appl. Math.
  doi: 10.1016/j.dam.2018.05.013
– year: 2020
  ident: CR4
  article-title: On the irregularity of -permutation graphs, Fibonacci cubes, and trees
  publication-title: Bull. Malays. Math. Sci. Soc.
  doi: 10.1007/s40840-020-00932-9
– volume: 39
  start-page: 12
  year: 2001
  end-page: 21
  ident: CR8
  article-title: On the Lucas cubes
  publication-title: Fibonacci Quart.
– volume: 11
  start-page: 235
  year: 1987
  end-page: 249
  ident: CR2
  article-title: Highly irregular graphs
  publication-title: J. Graph Theory
  doi: 10.1002/jgt.3190110214
– volume: 19
  start-page: 36
  year: 1988
  end-page: 42
  ident: CR5
  article-title: How to define an irregular graph
  publication-title: College Math. J.
  doi: 10.1080/07468342.1988.11973088
– volume: 25
  start-page: 505
  year: 2013
  end-page: 522
  ident: CR7
  article-title: Structure of Fibonacci cubes: a survey
  publication-title: J. Comb. Optim.
  doi: 10.1007/s10878-011-9433-z
– volume: 344–345
  start-page: 107
  year: 2019
  end-page: 115
  ident: CR9
  article-title: On some properties of graph irregularity indices with a particular regard to the -index
  publication-title: Appl. Math. Comput.
– volume: 266
  start-page: 191
  year: 2019
  end-page: 199
  ident: CR10
  article-title: Boundary enumerator polynomial of hypercubes in Fibonacci cubes
  publication-title: Discrete Appl. Math.
  doi: 10.1016/j.dam.2018.05.015
– volume: 19
  start-page: 36
  year: 1988
  ident: 981_CR5
  publication-title: College Math. J.
  doi: 10.1080/07468342.1988.11973088
– volume: 39
  start-page: 12
  year: 2001
  ident: 981_CR8
  publication-title: Fibonacci Quart.
– volume: 46
  start-page: 219
  year: 1997
  ident: 981_CR3
  publication-title: Ars Combin.
– volume: 4
  start-page: 3
  year: 1993
  ident: 981_CR6
  publication-title: IEEE Trans. Parallel Distrib. Syst.
  doi: 10.1109/71.205649
– volume: 25
  start-page: 505
  year: 2013
  ident: 981_CR7
  publication-title: J. Comb. Optim.
  doi: 10.1007/s10878-011-9433-z
– volume: 250
  start-page: 57
  year: 2018
  ident: 981_CR1
  publication-title: Discrete Appl. Math.
  doi: 10.1016/j.dam.2018.05.013
– volume: 11
  start-page: 235
  year: 1987
  ident: 981_CR2
  publication-title: J. Graph Theory
  doi: 10.1002/jgt.3190110214
– year: 2020
  ident: 981_CR4
  publication-title: Bull. Malays. Math. Sci. Soc.
  doi: 10.1007/s40840-020-00932-9
– volume: 344–345
  start-page: 107
  year: 2019
  ident: 981_CR9
  publication-title: Appl. Math. Comput.
– volume: 266
  start-page: 191
  year: 2019
  ident: 981_CR10
  publication-title: Discrete Appl. Math.
  doi: 10.1016/j.dam.2018.05.015
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SubjectTerms Applications of Mathematics
Cubes
Graph theory
Hypercubes
Irregularities
Mathematics
Mathematics and Statistics
Polynomials
Topology
Title The Irregularity Polynomials of Fibonacci and Lucas cubes
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