L(3,1)-Labeling of Double-Quadrilateral Windmill And Flower Graphs

Hafif Komarullah; Siti Zulfa Rosyidah; Rizqy Amalia Nurfadila; Mifdati Afifah

doi:10.20956/n3zjqz22

Authors

Hafif Komarullah Universitas Al-Falah As-Sunniyah
Siti Zulfa Rosyidah
Rizqy Amalia Nurfadila
Mifdati Afifah

DOI:

https://doi.org/10.20956/n3zjqz22

Keywords:

L(3,1)-labeling, double-quadrilateral windmill graph, double-quadrilateral flower graph

Abstract

The L(3,1)-labeling of a graph is a distance-constrained labeling in which adjacent vertices receive labels differing by at least 3, while vertices at distance two receive labels differing by at least 1. The minimum span among all such labelings, denoted by λ_3,1 (G), is called the L(3,1)-labeling number of G. In this paper, we determine the exact L(3,1)-labeling numbers of double-quadrilateral windmill graphs and double-quadrilateral flower graphs. By constructing feasible labelings and establishing sharp lower bounds, we prove that λ_3,1 (DQ_k)=3k+2 and λ_3,1 (FDQ_k)=2k+3 for every integer k≥2. These results provide the first L(3,1)-labeling characterization of these graph families and contribute to the study of distance-constrained graph labeling on graphs composed of interconnected quadrilateral cycles.

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