Commuting decomposition of Kn1,n2,...,nk through realization of the product A(G)A(GP k )

K. Arathi Bhat, G. Sudhakara

Research output: Contribution to journalArticle

Abstract

In this paper, we introduce the notion of perfect matching property for a k-partition of vertex set of given graph. We consider nontrivial graphs G and GP k , the k-complement of graph G with respect to a kpartition of V(G), to prove that A(G)A(GP k ) is realizable as a graph if and only if P satis-es perfect matching property. For A(G)A(GP k ) = A(Γ) for some graph Γ, we obtain graph parameters such as chromatic number, domination number etc., for those graphs and characterization of P is given for which GP k and Γ are isomorphic. Given a 1-factor graph G with 2n vertices, we propose a partition P for which GP k is a graph of rank r and A(G)A(GP k ) is graphical, where n ≤ r ≤ 2n. Motivated by the result of characterizing decomposable Kn,n into commuting perfect matchings [2], we characterize complete k-partite graph Kn1,n2,...,nk which has a commuting decomposition into a perfect matching and its k-complement.

Original languageEnglish
Pages (from-to)343-356
Number of pages14
JournalSpecial Matrices
Volume6
Issue number1
DOIs
Publication statusPublished - 01-01-2018

Fingerprint

Decompose
Graph in graph theory
Perfect Matching
Complement
Partition
Factor Graph
Domination number
Decomposable
Chromatic number
Isomorphic
If and only if
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

@article{ee67670172004920bc3075dae3da460f,
title = "Commuting decomposition of Kn1,n2,...,nk through realization of the product A(G)A(GP k )",
abstract = "In this paper, we introduce the notion of perfect matching property for a k-partition of vertex set of given graph. We consider nontrivial graphs G and GP k , the k-complement of graph G with respect to a kpartition of V(G), to prove that A(G)A(GP k ) is realizable as a graph if and only if P satis-es perfect matching property. For A(G)A(GP k ) = A(Γ) for some graph Γ, we obtain graph parameters such as chromatic number, domination number etc., for those graphs and characterization of P is given for which GP k and Γ are isomorphic. Given a 1-factor graph G with 2n vertices, we propose a partition P for which GP k is a graph of rank r and A(G)A(GP k ) is graphical, where n ≤ r ≤ 2n. Motivated by the result of characterizing decomposable Kn,n into commuting perfect matchings [2], we characterize complete k-partite graph Kn1,n2,...,nk which has a commuting decomposition into a perfect matching and its k-complement.",
author = "{Arathi Bhat}, K. and G. Sudhakara",
year = "2018",
month = "1",
day = "1",
doi = "10.1515/spma-2018-0028",
language = "English",
volume = "6",
pages = "343--356",
journal = "Special Matrices",
issn = "2300-7451",
publisher = "De Gruyter Open Ltd.",
number = "1",

}

Commuting decomposition of Kn1,n2,...,nk through realization of the product A(G)A(GP k ). / Arathi Bhat, K.; Sudhakara, G.

In: Special Matrices, Vol. 6, No. 1, 01.01.2018, p. 343-356.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Commuting decomposition of Kn1,n2,...,nk through realization of the product A(G)A(GP k )

AU - Arathi Bhat, K.

AU - Sudhakara, G.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper, we introduce the notion of perfect matching property for a k-partition of vertex set of given graph. We consider nontrivial graphs G and GP k , the k-complement of graph G with respect to a kpartition of V(G), to prove that A(G)A(GP k ) is realizable as a graph if and only if P satis-es perfect matching property. For A(G)A(GP k ) = A(Γ) for some graph Γ, we obtain graph parameters such as chromatic number, domination number etc., for those graphs and characterization of P is given for which GP k and Γ are isomorphic. Given a 1-factor graph G with 2n vertices, we propose a partition P for which GP k is a graph of rank r and A(G)A(GP k ) is graphical, where n ≤ r ≤ 2n. Motivated by the result of characterizing decomposable Kn,n into commuting perfect matchings [2], we characterize complete k-partite graph Kn1,n2,...,nk which has a commuting decomposition into a perfect matching and its k-complement.

AB - In this paper, we introduce the notion of perfect matching property for a k-partition of vertex set of given graph. We consider nontrivial graphs G and GP k , the k-complement of graph G with respect to a kpartition of V(G), to prove that A(G)A(GP k ) is realizable as a graph if and only if P satis-es perfect matching property. For A(G)A(GP k ) = A(Γ) for some graph Γ, we obtain graph parameters such as chromatic number, domination number etc., for those graphs and characterization of P is given for which GP k and Γ are isomorphic. Given a 1-factor graph G with 2n vertices, we propose a partition P for which GP k is a graph of rank r and A(G)A(GP k ) is graphical, where n ≤ r ≤ 2n. Motivated by the result of characterizing decomposable Kn,n into commuting perfect matchings [2], we characterize complete k-partite graph Kn1,n2,...,nk which has a commuting decomposition into a perfect matching and its k-complement.

UR - http://www.scopus.com/inward/record.url?scp=85053283777&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053283777&partnerID=8YFLogxK

U2 - 10.1515/spma-2018-0028

DO - 10.1515/spma-2018-0028

M3 - Article

AN - SCOPUS:85053283777

VL - 6

SP - 343

EP - 356

JO - Special Matrices

JF - Special Matrices

SN - 2300-7451

IS - 1

ER -