On exponential domination of some graphs
Küçük Resim Yok
Tarih
2016
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
InforMath Publishing Group
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let G be a graph and S ? V(G). We denote by <S> the subgraph of G induced by S. For each vertex u ? S and for each v ? V(G) - S, we define d¯(u,v) = d¯(v,u) to be the length of the shortest path in (V(G) - (S - {u})) if such a path exists, and ? otherwise. Let v ? V(G). We define ws(v) = ?2u?S 1/2d¯(u,u)-1 if v ? S, and ws(v) = 2 if v ? S. If, for each v ? V(G), we have ws(v) ? 1, then S is an exponential dominating set. The smallest cardinality of an exponential dominating set is the exponential domination number ?e(G). In this paper, we consider the exponential domination number in total graphs. We determine the exponential domination number of T(G) for some specific graphs G. © 2016 InforMath Publishing Group.
Açıklama
Anahtar Kelimeler
Domination, Exponential domination number, Graph vulnerability, Network design and communication, Total graph
Kaynak
Nonlinear Dynamics and Systems Theory
WoS Q Değeri
Scopus Q Değeri
Q3
Cilt
16
Sayı
1
