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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Apituley, Fredrylo Alberth Noel Joddy
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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ON THE IRREGULARITY STRENGTH AND MODULAR IRREGULARITY STRENGTH OF FRIENDSHIP GRAPHS AND ITS DISJOINT UNION Apituley, Fredrylo Alberth Noel Joddy; Talakua, Mozart W.; Lesnussa, Yopi Andry
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 3 (2022): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (513.763 KB) | DOI: 10.30598/barekengvol16iss3pp869-876

Abstract

For a simple, undirected graph G with, at most one isolated vertex and no isolated edges, a labeling f:E(G)→{1,2,…,k1} of positive integers to the edges of G is called irregular if the weights of each vertex of G has a different value. The integer k1 is then called the irregularity strength of G. If the number of vertices in G or the order of G is |G|, then the labeling μ:E(G)→{1,2,…,k2} is called modular irregular if the remainder of the weights of each vertex of G divided by |G| has a different value. The integer k2 is then called the modular irregularity strength of G. The disjoint union of two or more graphs, denoted by ‘+’, is an operation where the vertex and edge set of the result each be the disjoint union of the vertex and edge sets of the given graphs. This study discusses about the irregularity and modular irregularity strength of friendship graphs and some of its disjoint union, The result given is s(Fm ) = m + 1, ms(Fm ) = m + 1 and ms(rFm ) = rm + ⌈r/2⌉, where r denotes the number of copies of friendship graphs
Co-Authors Talakua, Mozart W. Yopi Andry Lesnussa