On the genus of non-zero component union graphs of vector spaces

Gnanappirakasam KALAİMURUGAN; Singaravelu GOPİNATH; T TAMİZH CHELVAM

doi:https://doi.org/10.15672/hujms.754535

Makale detayları

On the genus of non-zero component union graphs of vector spaces

Yazarlar:

Gnanappirakasam KALAİMURUGAN | Singaravelu GOPİNATH | T TAMİZH CHELVAM

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2021 Vol.50 Issue 6, pp.1595-1608

Belge Tipi:

Makale

Yayın Tarihi:

12/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000450401

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.754535

Özet:

 

Let VV\mathbb{V} be an nnn-dimensional vector space over the field FF\mathbb{F} with a basis B={α1,…,αn}.B={α1,…,αn}.\mathfrak{B}=\{\alpha_1,\ldots,\alpha_n\}. For a non-zero vector v∈V∖{0},v∈V∖{0},v\in\mathbb{V}\setminus\{0\}, the skeleton of vvv with respect to the basis BB\mathbb{B} is defined as SB(v)={αi:v=∑ni=1aiαi,ai≠0}.SB(v)={αi:v=∑i=1naiαi,ai≠0}.S_\mathfrak{B}(v)=\{\alpha_i : v=\sum_{i=1}^{n} a_i\alpha_i,  a_i\neq 0\}.  The non-zero component union graph Γ(VB)Γ(VB)\Gamma(\mathbb{V}_\mathfrak{B}) of VV\mathbb{V} with respect to BB\mathfrak{B} is the simple graph with vertex set V=V∖{0}V=V∖{0}V=\mathbb{V}\setminus\{0\} and two distinct non-zero vectors u,v∈Vu,v∈Vu,v \in V  are adjacent if and only if SB(u)∪SB(v)=B.SB(u)∪SB(v)=B.S_\mathfrak{B}(u)\cup S_\mathfrak{B}(v)=\mathfrak{B}. First, we obtain some graph theoretical properties of Γ(VB).Γ(VB).\Gamma(\mathbb{V}_\mathfrak{B}). Further, we characterize all finite dimensional vector spaces VV\mathbb{V} for which Γ(VB)Γ(VB)\Gamma(\mathbb{V}_\mathfrak{B}) has genus either 0 or 1 or 2. In the last part of the paper, we characterize all finite dimensional vector spaces VV\mathbb{V} for which the cross cap of Γ(VB)Γ(VB)\Gamma(\mathbb{V}_\mathfrak{B}) is 1.

Makale detayları

On the genus of non-zero component union graphs of vector spaces

Yazarlar: Gnanappirakasam KALAİMURUGAN | Singaravelu GOPİNATH | T TAMİZH CHELVAM

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2021 Vol.50 Issue 6, pp.1595-1608

Belge Tipi: Makale

Yayın Tarihi: 12/2021

Belge Dili: İngilizce

Document ID (Org No.): 2000450401

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

DOI: https://doi.org/10.15672/hujms.754535

Sayı

Yazarlar:

Gnanappirakasam KALAİMURUGAN | Singaravelu GOPİNATH | T TAMİZH CHELVAM

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2021 Vol.50 Issue 6, pp.1595-1608

Belge Tipi:

Makale

Yayın Tarihi:

12/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000450401

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.754535