On the modular irregularity strength of some graph classes
M A Shulhany1*, Y Rukmayadi2, A Maharani1, A Agusutrisno1, C Ahendyarti1, F Ikhsan1, N Nurhayati3, F Fardillah4, R N Ramadhan1, A V A Raissa1

1Faculty of Engineering, Universitas Sultan Ageng Tirtayasa, Jl. Jenderal Sudirman, KM. 3, Cilegon City 42435, Banten, Indonesia
2Faculty of Teacher Training and Education, Universitas Islam Negeri Sultan Maulana Hasanuddin, Jl. Jendral Sudirman No. 30, Serang City 42118, Banten, Indonesia
3Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Al Muslim, Jalan Almuslim, Bireuen 24261, Aceh, Indonesia
4Faculty of Engineering, Universitas Muhammadiyah Tangerang, Jl. Perintis Kemerdekaan I, No. 33, Tangerang 15118, Banten, Indonesia

Abstract

Let G be a simple graph of order n, with no component of order two. Define an edge l labeling . Let x in V(G), the weight of x is the sum of the l labels of all its incident edges. The edge l labeling is said modular irregular l labeling of G if there exists a bijective weight alpha function from V(G) to the group of integers modulo n. The smallest positive integer l such that G has a modular irregular l labeling is said the modular irregularity strength of G, denoted by ms(G). Write ms(G) is equal to infinity, if G has no modular irregular strength. We determine ms of some graph classes.

Keywords: graph, irregularity strength, modular irregularity strength

Topic: Mathematics