Lambda number of the reduced power graph of finite groups
Abstract
The reduced power graph ΓRP(G) of a group G is a simple graph with vertex set G, where two distinct vertices u and v are adjacent if and only if ⟨ u ⟩ ⊂ ⟨ v ⟩ or ⟨ v ⟩ ⊂ ⟨ u ⟩. An L(2,1)-labeling of a graph Γ is a mapping from the vertex set of Γ to the set of non-negative integers such that the labels of adjacent vertices differ by at least $2$ and the labels of vertices at distance two are distinct. The lambda number of Γ, denoted by λ(Γ), is defined as the minimum possible span of labels among all L(2,1)-labelings of Γ. In this paper, we establish upper and lower bounds for λ(ΓRP(G)) and characterize the conditions under which these bounds are achieved. As an application, we determine the exact value of λ(ΓRP(G)) for certain classes of finite groups.
Related
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BibTeX
@misc{malviy2026lambda,
title = {{Lambda number of the reduced power graph of finite groups}},
author = {Siddharth Malviy and Keerttiranjan Sahoo and Vipul Kakkar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25028},
eprint = {2610.25028},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25028},
}
RIS
TY - UNPB
TI - Lambda number of the reduced power graph of finite groups
AU - Siddharth Malviy
AU - Keerttiranjan Sahoo
AU - Vipul Kakkar
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25028
UR - https://arxiv.org/abs/2610.25028
AB - The reduced power graph Γ_RP(G) of a group G is a simple graph with vertex set G, where two distinct vertices u and v are adjacent if and only if ⟨ u ⟩ ⊂ ⟨ v ⟩ or ⟨ v ⟩ ⊂ ⟨ u ⟩. An L(2,1)-labeling of a graph Γ is a mapping from the vertex set of Γ to the set of non-negative integers such that the labels of adjacent vertices differ by at least $2$ and the labels of vertices at distance two are distinct. The lambda number of Γ, denoted by λ(Γ), is defined as the minimum possible span of labels among all L(2,1)-labelings of Γ. In this paper, we establish upper and lower bounds for λ(Γ_RP(G)) and characterize the conditions under which these bounds are achieved. As an application, we determine the exact value of λ(Γ_RP(G)) for certain classes of finite groups.
ER -