Product irregularity strength of certain graphs

Marcin Anholcer


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.
Author Marcin Anholcer (WIiGE / KBO)
Marcin Anholcer,,
- Department of Operations Research
Journal seriesArs Mathematica Contemporanea, ISSN 1855-3966, e-ISSN 1855-3974, (A 30 pkt)
Issue year2014
Publication size in sheets0.5
Keywords in EnglishProduct-irregular labeling, product irregularity strength, tree
ASJC Classification2602 Algebra and Number Theory; 2607 Discrete Mathematics and Combinatorics; 2608 Geometry and Topology; 2614 Theoretical Computer Science
Languageen angielski
Score (nominal)30
Score sourcejournalList
ScoreMinisterial score = 25.0, 02-01-2020, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 02-01-2020, ArticleFromJournal
Publication indicators WoS Citations = 3; Scopus SNIP (Source Normalised Impact per Paper): 2014 = 1.053; WoS Impact Factor: 2014 = 0.741 (2) - 2014=0.866 (5)
Citation count*6 (2020-09-10)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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