## Abstract

Let G be a graph with vertex set V (G) and edge set X(G). Consider the set A = {0, 1, 2}. A labeling f: V (G) → A induces a partial edge labeling f^{∗}: X(G) → A defined by f^{∗}(xy) = f(x), if and only if f(x) = f(y), for each edge xy ∈ X(G). For i ∈ A, let v_{f} (i) = |{v ∈ V (G): f(v) = i}| and e_{f}^{∗} (i) = |{e ∈ X(G): f^{∗} (e) = i}|. A labeling f of a graph G is said to be 3-vertex friendly if |v_{f} (i) − v_{f} (j)| ≤ 1, for all i ∈ {0, 1, 2}. The 3-vertex full balance index set of a graph G is denoted by F BI_{3v} (G) and is defined as {e_{f}^{∗}(i) − e_{f}^{∗}(j), for i, j = 0, 1, 2: f^{∗}runs over all 3-vertex friendly labeling f of G}. In paper, we study 3-vertex full balance index set and 3-vertex balance index set of some families of graph.

Original language | English |
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Pages (from-to) | 3247-3264 |

Number of pages | 18 |

Journal | Advances in Mathematics: Scientific Journal |

Volume | 9 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2020 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)