## Exponential Independence Number of Some Graphs

INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, cilt.29, ss.1151-1164, 2018 (SCI İndekslerine Giren Dergi)  • Cilt numarası: 29 Konu: 7
• Basım Tarihi: 2018
• Doi Numarası: 10.1142/s0129054118500260
• Dergi Adı: INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
• Sayfa Sayıları: ss.1151-1164

#### Özet

Let G be a graph and S subset of V(G). We define by < S > the subgraph of G induced by S. For each vertex u is an element of S and for each vertex v is an element of S\{u}, d((G, s\{u})())(u,v) is the length of the shortest path in < V(G) - ((S - {u}) - {v})> between u and v if such a path exists, and infinity otherwise. For a vertex u is an element of S, let omega((G, s\{u})) (u) = Sigma (v is an element of s\{u}) (1/2)(d) ((G, s\{u}) (u) (,v)-1) where (1/2)(infinity) = 0. Jager and Rautenbach  define a set S of vertices to be exponential independent if omega((G, s\{u})) (u) < 1 for every vertex u in S. The exponential independence number alpha(e)(G) of G is the maximum order of an exponential independent set. In this paper, we give a general theorem and we examine exponential independence number of some tree graphs and thorn graph of some graphs.