## Abstract

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 language | English |
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Article number | 012009 |

Journal | Journal of Physics: Conference Series |

Volume | 1836 |

Issue number | 1 |

DOIs | |

Publication status | Published - 23 Mar 2021 |

Event | 4th International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2020 - Jember, East Java, Indonesia Duration: 22 Aug 2020 → 23 Aug 2020 |