Common closed neighbourhood prime labeling

Rinurwati, A. S. Alfiyani

Research output: Contribution to journalConference articlepeer-review


Let G = (VG,EG ) be a connected graph of order n. A bijectiong: VG ? {1,2,3,... ,n} is said to be prime labeling if for each two distinct vertices a,b ?Vc which a is adjacent to b, gcd(g(a),g(b)) = 1. A graph that satisfies the prime labeling is called a prime graph. Graph G is a neighbourhood prime graphif there is a bijection g: VG? {1,2,3, ...,n} so that for each vertex a V Gwith deg(a) > 1, gcd{g(b): B ? N(a)} = 1. Graphs that have neighbourhood-prime labeling are called neighbourhood prime graphs. In this paper, we introduce a new variant of labelingas a development of prime labeling and neighbourhood prime labeling called common-closed-neighbourhood prime labeling. A bijection g: VG ? {1,2,3, ...,n} is said to be common closed neighbourhood prime labeling if for each two distinct vertices a,b ?VG which a is adjacent to b, gcd{g(c):c ? N[a,b]} = 1, where N[a,b] = N[a] n N[b]. A common-closed-neighbourhood prime graph is a graph that satisfies the common closed neighborhood prime labeling. Also, we studied an algorithm for some graphs which admits common closed neighbourhood prime labeling.

Original languageEnglish
Article number012009
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 23 Mar 2021
Event4th International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2020 - Jember, East Java, Indonesia
Duration: 22 Aug 202023 Aug 2020


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