The domination number of a graph G is the smallest number of vertices which dominate all
remaining vertices by edges of G. The bondage number of a nonempty graph G is the …

Given a graph Γ, a subset C of V(Γ) is called a perfect code in Γ if every vertex of Γ is at
distance no more than one to exactly one vertex in C, and a subset C of V(Γ) is called a total …

A perfect code in a graph Γ=(V, E) is a subset C of V such that no two vertices in C are
adjacent and every vertex in V∖ C is adjacent to exactly one vertex in C. A subgroup H of a …

Let Γ be a graph with vertex set V(Γ). A subset C of V(Γ) is called a perfect code in Γ if C is an
independent set of Γ and every vertex in V(Γ)∖C is adjacent to exactly one vertex in C. A …

The rank modulation scheme has been proposed for efficient writing and storing data in
nonvolatile memory storage. Error correction in the rank modulation scheme is done by …

Let S be a subset of finite cyclic group Z n not containing the identity element 0 with S=− S.
Cayley graphs on Z n with respect to S are called circulant graphs and denoted by Cay (Z n …

A perfect code in a graph Γ=(V, E) is a subset C of V that is an independent set such that
every vertex in V∖ C is adjacent to exactly one vertex in C. A total perfect code in Γ is a …

Let Γ be a graph with vertex set V, and let a, b be nonnegative integers. An (a, b)-regular set
in Γ is a nonempty proper subset D of V such that every vertex in D has exactly a neighbours …

Abstract A subset S⊆ V in a graph G=(V, E) is a [j, k]-set if, for every vertex v∈ V∖ S, j≤| N
(v)∩ S|≤ k for non-negative integers j and k, that is, every vertex v∈ V∖ S is adjacent to at …

Domination is an important property in the design of efficient computer interconnection
networks. We provide a complete characterization of circulant graphs with two chord lengths …