Year: 2025
Type: article
Abstract: For j ≤ k, the L(j, k)- labeling problem arose form the code assignment problem of the wireless network. That is, let n,j,k be non-negative real numbers with j ≤ k, an n-L(j, k)-labeling of a graph G is mapping f: V(G)→[0, n] such that |f(u)-f(v)| ≥ j if d(u, v)=1, and |f(u)-f(v)|≥k if t d(u, v)=2. The span of f is the difference between the maximum and minimum labeling numbers assigned by f. The L(j, k)-labeling number of graph G, denoted by λ(j,k) (G), is the minimum span of all L(j, k)-labeling of G. The infinite distance graph, denoted by D (d1,d2,…,dk), has the set Z of integers as a vertex set and in which two vertices i,j∈Z are adjacent if and only if |i-j|∈D. The finite distance graph, denoted by Dn (d1,d2,…,dk), is the subgraph of D(d1,d2,…,dk) induced by vertices {0,1,…,n-1}. This paper determines the L(j, k)-labeling number and the circular L(j, k)-labeling number of distance graph Dn (1,5) for 2j ≤ k.
Authors: He Shuping, Wu Qiong
Institution: Tianjin University of Technology and Education
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408106274