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The Edge-Balanced Properties of Product Graphs of Paths

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Journal of Mathematical Research with Applications 2023年第1期43卷 25-39页

作者： Zhenbin GAO Wei QIU Sin-Min LEE College of Mathematical Sciences Harbin Engineering University 1786 Plan Tree Drive

In 2009, Kwong and Lee considered a new labeling problem of graph theory–the edge-balance index set of graph. In this paper, we investigated the edge-balanced properties of product of paths by using a method known as... 详细信息

关键词： vertex labeling edge labeling embedding graph boundary vertex inner vertex P_m × P_n

Full Friendly Index Sets of Cartesian Products of Two Cycles

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Acta Mathematica Sinica,English Series 2010年第7期26卷 1233-1244页

作者： Wai chee SHIU Department of Mathermatics Hong Kong Baptist University

Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊： E → Z2 defined by f＊（xy） = f（x）＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i... 详细信息

Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊： E → Z2 defined by f＊（xy） = f（x）＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i） = ｜f＊^-1（i）｜. A labeling f is called friendly if ｜vf（1） - vf（0）｜ ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if（G） = e（1） - el（0）. The set [if（G）｜ f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI（G）. In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.

关键词： vertex labeling friendly labeling friendly index set Cartesian product of two cycles

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On Friendly Index Sets of Cyclic Silicates

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Journal of Mathematical Research with Applications 2015年第6期35卷 591-604页

作者： Zhenbin GAO Sinmin LEE Guangyi SUN Geechoon LAU College of Science Harbin Engineering University Deptartment of Computer Science San Jose State University Faculty of Computer and Mathematical Sciences Universiti Teknologi MARA (Segamat Campus)

Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) →Z2 induces an edge labeling f*: E(G) → Z2 defined by f*(xy) = f(x) + f(y), for each edge xy ∈ E(G). For i ∈ Z2, let vf(i) = |{v ∈ V(G) : f(v) = i}| and ef(i) = |{e ∈ E(G) : f*(e) =i}|. A labeling f of a graph G is said to be friendly if |vf(0)- vf(1)| ≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as {|ef(0)- ef(1)|: the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS(n, m).

关键词： vertex labeling friendly labeling cordiality friendly index set cycle CS(n,m) arithmetic progression

Full Friendly Index Sets of a Family of Cubic Graphs

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Chinese Quarterly Journal of Mathematics 2021年第3期36卷 221-234页

作者： BAI Yu-jie WU Shu-fei School of Mathematics and Information Science Henan Polytechnic UniversityJiaozuo 454003China

Let G=(V,E)be a *** a vertex labeling f:V→Z2,it induces an edge labeling f+:E→Z2,where for each edge v1 v2∈E we have f+(v1 v2)=f(v1)+f(v2).For each i∈Z2,we use vf(i)(respectively,ef(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 *** full friendly index set of a graph G,denoted by F F I(G),consists of all possible values of ef(1)-ef(0),where f ranges over all friendly labelings of *** this paper,motivated by a problem raised by[6],we study the full friendly index sets of a family of cubic graphs.

关键词： vertex labeling Friendly labeling Embedding labeling graph method Cubic graph

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