1-edge balance index sets of C_n tines P_3 and K_{n,n}
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Let G be a graph with vertex set V , edge set E and Z2 = {0, 1}. Let f be a labeling from E to Z2, so that the labels of the edges are 0 or 1. The edges labelled 1 are called 1-edges and edges labelled 0 are called 0-edges. The edge labeling f induces a vertex labeling f : V −! Z2 defined by f(v) = ( 1 if the number of 1-edges incident on v is odd, 0 if the number of 1-edges incident on v is even. For i 2 Z2 let ef (i) = e(i) = card{e 2 E : f(e) = i} and vf (i) = v(i) = card{v 2 V : f(v) = i}. A labeling f is said to be edge-friendly if | e(0) − e(1) | 1. The 1- edge balance index set (OEBI) of a graph G is defined by {| vf (0) − vf (1) | : the edge labeling f is edge-friendly}. The main purpose of this paper is to completely determine the 1-edge balance index sets of Cn × P3, Kn,n.
Abstract
Let G be a graph with vertex set V , edge set E and Z2 = {0, 1}. Let f be a labeling from E to Z2, so that the labels of the edges are 0 or 1. The edges labelled 1 are called 1-edges and edges labelled 0 are called 0-edges. The edge labeling f induces a vertex labeling f : V −! Z2 defined by f(v) = ( 1 if the number of 1-edges incident on v is odd, 0 if the number of 1-edges incident on v is even. For i 2 Z2 let ef (i) = e(i) = card{e 2 E : f(e) = i} and vf (i) = v(i) = card{v 2 V : f(v) = i}. A labeling f is said to be edge-friendly if | e(0) − e(1) | 1. The 1- edge balance index set (OEBI) of a graph G is defined by {| vf (0) − vf (1) | : the edge labeling f is edge-friendly}. The main purpose of this paper is to completely determine the 1-edge balance index sets of Cn × P3, Kn,n.
참고문헌 (7)
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