On Edge-balance Index Sets of N cycles Three Nested Graph (n = 0, 1, 2 (mod6))
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Let G be a simple graph with vertex set V (G) and edge set E(G), and let Z_2 ={0, 1}. For a given binary labeling f : E(G) → Z_2, the edge labeling f induces a partial vertex labeling f^* : V (G) → Z_2 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 not de¯ned. For i ∈ Z_2, let vf (i) = v(i) = card{v ∈V (G) : f^*(v) = i} and ef (i) = e(i) = card{e ∈ E(G) : f(e) = i}. The edge-balance index set of the graph G, EBI(G), is de¯ned as {|vf (0)-vf (1)| :the edge labeling f is edge-friendlyg. The graph C_n × P_3 is said that three cycles are linked with n paths. In this paper,we will research a structural method of the edge-balance index set of n cycles three nested graph (n≡0, 1, 2(mod6)).
Abstract
Let G be a simple graph with vertex set V (G) and edge set E(G), and let Z_2 ={0, 1}. For a given binary labeling f : E(G) → Z_2, the edge labeling f induces a partial vertex labeling f^* : V (G) → Z_2 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 not de¯ned. For i ∈ Z_2, let vf (i) = v(i) = card{v ∈V (G) : f^*(v) = i} and ef (i) = e(i) = card{e ∈ E(G) : f(e) = i}. The edge-balance index set of the graph G, EBI(G), is de¯ned as {|vf (0)-vf (1)| :the edge labeling f is edge-friendlyg. The graph C_n × P_3 is said that three cycles are linked with n paths. In this paper,we will research a structural method of the edge-balance index set of n cycles three nested graph (n≡0, 1, 2(mod6)).
참고문헌 (7)
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