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 …

More than 50 years ago, Golomb and Welch conjectured that there is no perfect Lee codes
of packing radius in for and. Recently, Leung and the second author proved that if is linear …

Error-correcting codes were introduced to combat errors in communication channels,
storage devices, and other computerized systems. In each such system, the information may …

It is conjectured by Golomb and Welch around half a century ago that there is no perfect Lee
codes of packing radius in for and. In 2020, Leung and Zhou proved this conjecture for linear …

We derive eigenvalue bounds for the $ t $-distance chromatic number of a graph, which is a
generalization of the classical chromatic number. We apply such bounds to hypercube …

Abstract In 1968, Golomb and Welch conjectured that there is no perfect Lee codes with
radius r≥ 2 and dimension n≥ 3. A diameter perfect code is a natural generalization of the …

We prove the nonexistence of lattice tilings of Z n by Lee spheres of radius 2 for all
dimensions n≥ 3. This implies that the Golomb-Welch conjecture is true when the common …

In 1968, Golomb and Welch conjectured that there is no perfect Lee codes with radius $
r\ge2 $ and dimension $ n\ge3 $. A diameter perfect code is a natural generalization of the …

In a graph Γ with vertex set V, a subset C of V is called an (a, b)-regular set if every vertex in
C has exactly a neighbors in C and every vertex in V\C has exactly b neighbors in C, where …