Product irregularity strength of certain graphs

Marcin Anholcer

Abstract


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.


Keywords


Product-irregular labeling, product irregularity strength, tree

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DOI: https://doi.org/10.26493/1855-3974.258.2a0

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications