A Note on 1-edge balance index set

Let G be a graph with vertex set V and edge set E, and [Z.sub.2] = {0, 1}. Let f be a labeling from E to [Z.sub.2], 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 ⊂ [Z.su...

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Bibliographic Details
Published inInternational journal of mathematical combinatorics Vol. 3; p. 113
Main Authors Adiga, Chandrashekar, A.S., Shrikanth, C.S., Shivakumar Swamy
Format Journal Article
LanguageEnglish
Published Gallup Neutrosophic Sets and Systems 01.09.2012
Science Seeking - distributor
Subjects
Combinatorics
Fuzzy sets
Graph theory
Graphs
Number theory
Set theory
India
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Summary:Let G be a graph with vertex set V and edge set E, and [Z.sub.2] = {0, 1}. Let f be a labeling from E to [Z.sub.2], 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 ⊂ [Z.sub.2] defined by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] For i ∈ [Z.sub.2] let [e.sub.f] (i) = e(i) = |{e [member of] E: f (e) = i}| and [v.sub.f] (i) = v(i) = |{v ∈ V: f* (v) = i}|. A labeling f is said to be edge-friendly if | e(0) - e(1) |[less than or equal to] 1. The 1-edge balance index set (OEBI) of a graph G is defined by {| [v.sub.f] (0) - [v.sub.f] (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. Key Words: Mycielskian graph, edge labeling, edge-friendly, 1-edge balance index set, Smarandachely induced vertex labeling, Smarandachely edge-friendly graph. AMS(2010): 05C78
ISSN:1937-1055
1937-1047