A Note on 1-Edge Balance Index Set

Adiga, Chandrashekar and Shrikanth, A. S. and Shivakumar Swamy, . (2012) A Note on 1-Edge Balance Index Set. International Journal of Mathematical Combinatorics, 3. pp. 113-117. ISSN 1937 - 1055

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Let G be a graph with vertex set V and 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 . Z2 let ef (i) = e(i) = |{e . E : f(e) = i}| and vf (i) = v(i) = |{v . 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 set of wheel and Mycielskian graph of a path.

Item Type: Article
Subjects: E Mathematical Science > Mathematics
Divisions: Department of > Mathematics
Depositing User: C Swapna Library Assistant
Date Deposited: 28 Aug 2019 06:04
Last Modified: 08 Jul 2022 11:03
URI: http://eprints.uni-mysore.ac.in/id/eprint/7206

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