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Published in:   Vol. 2 Issue 1 Date of Publication:   June 2013

Edge -Balance Index Sets of HELM

V.Sharon Philomena,K.Thirusangu

Page(s):   65-67 ISSN:   2278-2397
DOI:   10.20894/IJCOA.101.002.001.018 Publisher:   Integrated Intelligent Research (IIR)

The edge-balance index set of a graph G (V, E) was defined by Chopra, Lee and Su[1] in 2010 as follows: For an edge labeling f:E(G)→{0,1}, a partial vertex labeling f * : V(G) → {0, 1} is defined as 0 , if more edges with label 0 are incident to v f * (v) = 1 , if more edges with label 1 are incident to v unlabeled , otherwise For i = 0 or 1, let A = {uv ∈ E : f(uv) = i} and B = {v ∈ V : f *(v) = i} Let eG (i) = |A| and vG (i) = |B|. The edge balance index set of G denoted as EBI(G) is computed as EBI(G)={|vG(0) vG(1)|: the edge labeling f satisfies |eG(0) eG(1)| ≤1}. The edge-balance index set for the fan graph Fn-1 where Fn-1 = Pn-1+K1 and wheel graph Wn, where Wn = Cn-1 + K1 was obtained by Lee, Tao, Lo[5]. In this paper, we compute the edge-balance index set for the Helm graph, where the Helm graph is defined as the graph obtained from a wheel graph by attaching a pendant edge at each vertex of the n- cycle.