Fractional strong metric dimension of convex polytopes and its applications

Faiza Jamil; Agha Kashif; Sohail Zafar

Makale detayları

Fractional strong metric dimension of convex polytopes and its applications

Yazarlar:

Faiza Jamil | Agha Kashif | Sohail Zafar

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.389-403

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001346351

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 The fractional versions of various metric related parameters have recently gained importance due to their applications in the fields of sensor networking, robot navigation and linear optimization problems. Convex polytopes are collection of those polytopes of Euclidean space which are their convex subsets. They have key importance in the field of network designing due to their stable and resilient structure which aids optimal data transfer. The identification and removal of components nodes of a communication network causing abruption in its flow is of key importance for optimal data transmission. These components are referred as strong resolving neighbourhood SRNs in graph theory and assigning least weight to these components aids the computation of fractional strong metric dimension FSMD. In this paper, we compute FSMD for certain convex polytopes which include mathbbP_n, mathbbP_n1 and mathbbP_n2. In this regard, it is shown that for n geq 3, FSMD of mathbbP_n and mathbbP_n2 is n and frac3n2, respectively. Also, FSMD of mathbbP_n1 is n when n is odd and frac3n2 when n is even. Finally, an application of FSMD in the context of internet connection networks is furnished.

 The fractional versions of various metric related parameters have recently gained importance due to their applications in the fields of sensor networking, robot navigation and linear optimization problems. Convex polytopes are collection of those polytopes of Euclidean space which are their convex subsets. They have key importance in the field of network designing due to their stable and resilient structure which aids optimal data transfer. The identification and removal of components nodes of a communication network causing abruption in its flow is of key importance for optimal data transmission. These components are referred as strong resolving neighbourhood SRNs in graph theory and assigning least weight to these components aids the computation of fractional strong metric dimension FSMD. In this paper, we compute FSMD for certain convex polytopes which include mathbbP_n, mathbbP_n1 and mathbbP_n2. In this regard, it is shown that for n geq 3, FSMD of mathbbP_n and mathbbP_n2 is n and frac3n2, respectively. Also, FSMD of mathbbP_n1 is n when n is odd and frac3n2 when n is even. Finally, an application of FSMD in the context of internet connection networks is furnished.

 The fractional versions of various metric related parameters have recently gained importance due to their applications in the fields of sensor networking, robot navigation and linear optimization problems. Convex polytopes are collection of those polytopes of Euclidean space which are their convex subsets. They have key importance in the field of network designing due to their stable and resilient structure which aids optimal data transfer. The identification and removal of components nodes of a communication network causing abruption in its flow is of key importance for optimal data transmission. These components are referred as strong resolving neighbourhood SRNs in graph theory and assigning least weight to these components aids the computation of fractional strong metric dimension FSMD. In this paper, we compute FSMD for certain convex polytopes which include mathbbP_n, mathbbP_n1 and mathbbP_n2. In this regard, it is shown that for n geq 3, FSMD of mathbbP_n and mathbbP_n2 is n and frac3n2, respectively. Also, FSMD of mathbbP_n1 is n when n is odd and frac3n2 when n is even. Finally, an application of FSMD in the context of internet connection networks is furnished.

 The fractional versions of various metric related parameters have recently gained importance due to their applications in the fields of sensor networking, robot navigation and linear optimization problems. Convex polytopes are collection of those polytopes of Euclidean space which are their convex subsets. They have key importance in the field of network designing due to their stable and resilient structure which aids optimal data transfer. The identification and removal of components nodes of a communication network causing abruption in its flow is of key importance for optimal data transmission. These components are referred as strong resolving neighbourhood SRNs in graph theory and assigning least weight to these components aids the computation of fractional strong metric dimension FSMD. In this paper, we compute FSMD for certain convex polytopes which include mathbbP_n, mathbbP_n1 and mathbbP_n2. In this regard, it is shown that for n geq 3, FSMD of mathbbP_n and mathbbP_n2 is n and frac3n2, respectively. Also, FSMD of mathbbP_n1 is n when n is odd and frac3n2 when n is even. Finally, an application of FSMD in the context of internet connection networks is furnished.

Makale detayları

Fractional strong metric dimension of convex polytopes and its applications

Yazarlar:

Faiza Jamil | Agha Kashif | Sohail Zafar

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.389-403

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001346351

pISSN:

2651-477X

convex polytope

metric dimension

fractional strong metric dimensionconvex polytope

metric dimension

fractional strong metric dimension.

Sayı

Makale detayları

Fractional strong metric dimension of convex polytopes and its applications

Yazarlar: Faiza Jamil | Agha Kashif | Sohail Zafar

Yayıncı: Hacettepe University

Ana Başlıklar: Mathematical Sciences

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.389-403

Belge Tipi: Makale

Yayın Tarihi: 4/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001346351

pISSN: 2651-477X

convex polytope

metric dimension

fractional strong metric dimensionconvex polytope

metric dimension

fractional strong metric dimension.

Sayı

Yazarlar:

Faiza Jamil | Agha Kashif | Sohail Zafar

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.389-403

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001346351

pISSN:

2651-477X