Devadas, N C and Gowtham, H J and Dsouza, Sabitha and Bhat, Pradeep G
(2020)
*Vertex full balance index set of graphs.*
Advances in Mathematics: Scientiﬁc Journal, 9 (6).
pp. 3247-3264.
ISSN 2332-2071

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## Abstract

Let G beagraphwithvertexset V (G) andedgeset 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 vf(i) = |{v ∈ V (G) : f(v) = i}| and ef∗(i) = |{e ∈ X(G) : f∗(e) = i}|. Alabelingf ofagraphGissaidtobe3-vertexfriendly if|vf(i)−vf(j)|≤ 1, for all i ∈{0,1,2}. The 3-vertex full balance index set of a graph G is denoted by FBI3v(G) and is deﬁned as{ef∗(i)−ef∗(j),for i,j = 0,1,2 : f∗ runs over all 3-vertex friendly labeling f of G}. In paper, we study 3vertex full balance index set and 3-vertex balance index set of some families of graph.

Item Type: | Article |
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Subjects: | Engineering > MIT Manipal > Mathematics |

Depositing User: | MIT Library |

Date Deposited: | 21 Aug 2020 09:14 |

Last Modified: | 21 Aug 2020 09:14 |

URI: | http://eprints.manipal.edu/id/eprint/155567 |

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