Geodesic
S4-decomposition of the line graph of the complete graph
Serdica Mathematical Journal, Tome 47 (2022) no. 4, pp. 273-284 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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Let \(S_{k}\) denote a star with \(k\) edges. The line graph of the complete graph \(K_{n}\) is denoted by \(L(K_{n})\). In this paper, we prove that the graph \(L(K_{n})\) has an \(S_{4}\)-decomposition if and only if $n\geq 6$ and \(n\equiv 0,1,2,4,6 \pmod 8\).
Keywords: decomposition, induced subgraph, line graph, complete graph, star, 05C70, 05C76 
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     title = {S4-decomposition of the line graph of the complete graph},
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Arthi, Kulandaivelu; Sangeetha, Renganathan; Sankari, C. S4-decomposition of the line graph of the complete graph. Serdica Mathematical Journal, Tome 47 (2022) no. 4, pp. 273-284. http://geodesic.mathdoc.fr/item/SMJ2_2022_47_4_a0/