Geodesic
Product irregularity strength of certain graphs
Ars Mathematica Contemporanea, Tome 7 (2014) no. 1, pp. 23-29.

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Consider a simple graph G with no isolated edges and at most one isolated vertex. A labeling w: E(G) → {1, 2, …, m} is called product - irregular, if all product degrees pdG(v) = ∏ e ∋ vw(e) are distinct. The goal is to obtain a product - irregular labeling that minimizes the maximal label. This minimal value is called the product irregularity strength and denoted ps(G). We give the exact values of ps(G) for several families of graphs, as complete bipartite graphs Km, n, where 2 ≤ m ≤ n ≤ (m + 2) choose 2, some families of forests, including complete d-ary trees, and other graphs with δ(G) = 1.
DOI : 10.26493/1855-3974.258.2a0
Keywords: Product-irregular labeling, product irregularity strength, tree 
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Marcin Anholcer. Product irregularity strength of certain graphs. Ars Mathematica Contemporanea, Tome 7 (2014) no. 1, pp. 23-29. doi : 10.26493/1855-3974.258.2a0. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.258.2a0/

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