Full Friendly Index Sets of a Family of Cubic Graphs

BAI Yu-jie, WU Shu-fei

doi:10.13371/j.cnki.chin.q.j.m.2021.03.001

Chinese Quarterly Journal of Mathematics >

2021 , Vol. 36 >Issue 3: 221 - 234

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.03.001

Full Friendly Index Sets of a Family of Cubic Graphs

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School of Mathematics and Information Science, Henan Polytechnic University

BAI Yu-jie (1995-), famale, native of Zhangjiakou, Hebei, postgraduate student of Henan Polytechnic University, engages in graph theory; WU Shu-fei (1989-), male, native of Jiaozuo, Henan, lecture of Henan Polytechnic University, Ph.D, engages in graph theory.

Received date: 2021-05-21

Online published: 2021-10-08

Supported by

Supported by the National Natural Science Foundation of China (Grant No. 11801149);
Doctoral Fund of Henan Polytechnic University (Grant No. B2018-55).

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Abstract

Let G =( V,E ) be a graph. For a vertex labeling f : V →Z₂ , it induces an edge labeling f ⁺ : E→Z ₂ , where for each edge v ₁ v ₂ ∈E we have f ⁺ ( v ₁ v ₂ )= f ( v ₁ )+ f ( v ₂ ). For each i∈Z ₂, we use v_f( i ) (respectively, e _f ( i )) to denote the number of vertices (respectively, edges) with label i . A vertex labeling f of G is said to be friendly if vertices with different labels differ in size by at most one. The full friendly index set of a graph G , denoted by FFI ( G ), consists of all possible values of e _f (1) −e _f (0), where f ranges over all friendly labelings of G . In this paper, motivated by a problem raised by [6], we study the full friendly index sets of a family of cubic graphs.

Key words： Vertex labeling; Friendly labeling; Embedding labeling graph method; Cubic graph

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BAI Yu-jie, WU Shu-fei . Full Friendly Index Sets of a Family of Cubic Graphs[J]. Chinese Quarterly Journal of Mathematics, 2021 , 36(3) : 221 -234 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.001

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