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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Mifdati Afifah
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Mathematics

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L(3,1)-Labeling of Double-Quadrilateral Windmill And Flower Graphs Hafif Komarullah; Siti Zulfa Rosyidah; Rizqy Amalia Nurfadila; Mifdati Afifah
Jurnal Matematika, Statistika dan Komputasi Vol. 23 No. 1 (2026): September 2026
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/n3zjqz22

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.
Co-Authors Hafif Komarullah Rizqy Amalia Nurfadila Siti Zulfa Rosyidah