The diameter vulnerability of the generalized Petersen graph GP[tk,k]GP[tk,k]{GP[tk,k]}

GÜLNAZ BORUZANLI EKİNCİ; JOHN BAPTIST GAUCI

Makale detayları

The diameter vulnerability of the generalized Petersen graph GP[tk,k]GP[tk,k]{GP[tk,k]}

Yazarlar:

GÜLNAZ BORUZANLI EKİNCİ | JOHN BAPTIST GAUCI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 6, pp.2897-2915

Belge Tipi:

Makale

Yayın Tarihi:

11/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745716

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

The diameter of a graph gives the length of the longest path among all the shortest paths between any two vertices of the graph, and the diameter vulnerability problem measures the change in the diameter upon the deletion of edges. In this paper we determine the diameter vulnerability of the generalized Petersen graph GP[tk,k]GP[tk,k]GP[tk,k], for integers t≥2t≥2t\geq 2 and k≥1k≥1k\geq 1, and show that (except for some small cases) the diameter remains unchanged upon the deletion of one edge. This work contributes towards a solution of the well-known (Δ,D,D′,s)(Δ,D,D′,s)(\Delta, D, D', s)-problem, which attempts to find large graphs with maximum degree ΔΔ\Delta and diameter DDD such that the subgraphs obtained by deleting any set of up to sss edges have diameter at most D′D′D', preferably equal to DDD itself. In cases when the delay in communication across a network is directly related to the length of the paths between stations, network designers generally prefer to opt for graphs having the property of being resistant to drastic shocks upon the deletion of edges. This reliability property makes this class of graphs ideal to be used for modeling interconnection networks.

Makale detayları

The diameter vulnerability of the generalized Petersen graph GP[tk,k]GP[tk,k]{GP[tk,k]}

Yazarlar: GÜLNAZ BORUZANLI EKİNCİ | JOHN BAPTIST GAUCI

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 6, pp.2897-2915

Belge Tipi: Makale

Yayın Tarihi: 11/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745716

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

GÜLNAZ BORUZANLI EKİNCİ | JOHN BAPTIST GAUCI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 6, pp.2897-2915

Belge Tipi:

Makale

Yayın Tarihi:

11/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745716

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098