Distance two labeling of direct product of paths and cycles

2013/11/16 by Deborah Olayide Ajayi, Ajayi, Deborah O. A., Tayo Charles Adefokun +1
Computer Science · Engineering · #05C78 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1311.4090

openalex publication_date 2013/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that [n]=\0,1,2,...,n\ is a set of non-negative integers and h,k ∈ [n]. The L(h,k)-labeling of graph G is the function l:V(G)→[n] such that |l(u)-l(v)|≥ h if the distance d(u,v) between u and v is one and |l(u)-l(v)| ≥ k if the distance d(u,v) is two. Let L(V(G))=\l(v): v ∈ V(G)\ and let p be the maximum value of L(V(G)). Then p is called λ_h^k-number of G if p is the least possible member of [n] such that G maintains an L(h,k)-labeling. In this paper, we establish λ₁¹- numbers of P _m × C_n graphs for all m ≥ 2 and n≥ 3.

Related

• Distance-two labelings of digraphs
• Optimal L(d,1)-labeling of certain direct graph bundles cycles over cycles and Cartesian graph bundles cycles over cycles
• Distance labelings: a generalization of Langford sequences
• Graph Labeling with Distance Conditions and the Delta Squared Conjecture
• Optimal L(2,1)-labeling of certain strong graph bundles cycles over cycles