On Edge-Balance Index Sets of the Graph C_nxP₆(n=3,4,5mod6)

Abstract:

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 C_nxP ₆(n=3,4,5mod6).

• Periodical: Advanced Materials Research (Volume 339)
• Pages: 662-665
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.339.662
• Online since: September 2011
• Authors: Yu Rong Ji, Ai Jun Li, Jing Jing Yao
• Keywords: Edge Labeling, Edge-Balance Index Set, Edge-Friendly

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