scholarly journals Research on the Quick Construction of the Edge-balance Index Sets of a Nested Graph with Infinite Paths and Power Circles

2012 ◽  
Vol 4 (10) ◽  
pp. 40-46
Author(s):  
Hongjuan Tian ◽  
Yuge Zheng
Keyword(s):  
Index Sets ◽  
Balance Index

On Edge-Balance Index Sets of the Graph CnxP6(n=3,4,5mod6)

2011 ◽  
Vol 339 ◽  
pp. 662-665
Author(s):  
Yu Rong Ji ◽  
Ai Jun Li ◽  
Jing Jing Yao
Keyword(s):  
Simple Graph ◽  
Index Sets ◽  
Vertex Set ◽  
Binary Edge ◽  
Balance Index ◽  
Edge Labeling

Let G be a simple graph with vertex set V(G) and edge set E(G), and let Z2 = {0,1}. For a given binary edge labeling f :E(G)→Z2 , the edge labeling f induces a partial vertex labeling f*:V(G)→Z2 such that f*(v) =1(0) iff the number of 1-edges (0-edges) is strictly greater than the number of 0-edges (1-edges) incident to v , otherwise f*(v) is idefined. For i∈Z2 , let v(i)=card{v∈V(G): f*(v) =i} and e(i) = card{e∈E(G) : f (e)=i}. The edge-balance index sets of a graph G,EBI(G), is defined as {|v(0) −v(1) |: the edge labeling f satisfies |e(0)−e(1) |≤1}.In this paper, we completely determine the edge-balance CnxP 6(n=3,4,5mod6).

Edge -Balance Index Sets of HELM

2013 ◽  
Vol 2 (1) ◽  
pp. 65-67
Author(s):  
Jeba Jesintha J ◽  
Keyword(s):  
Index Sets ◽  
Balance Index

On Edge-Balance Index Sets of a Nested Graph with Infinite Paths and Power Circles

2013 ◽  
Vol 340 ◽  
pp. 561-566
Author(s):  
Hong Juan Tian ◽  
Yu Ge Zheng
Keyword(s):  
Index Set ◽  
Index Sets ◽  
Class Graph ◽  
Balance Index

We generalize the concept of edge-balanced labeling to the concept of edge-balance index set of graphs. In this article, we define all class of the nested graph with infinite for the integer and investigate the edge-balance index set of a class graph. In particular, we completely determine the edge-balance index sets of the class graph for the integer and solve formula proof and graphic tectonic methods.

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