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National Academy Science Letters

, Volume 41, Issue 4, pp 239–242 | Cite as

Vertex Equitable Labeling of Signed Bistars

  • Rashmi Jain
  • Mukti Acharya
  • Sangita Kansal
Short Communication
  • 40 Downloads

Abstract

A signed graph \(S=(S^u,\sigma )\) has a graph \(S^u\) and a function \(\sigma :E(S^u)\longrightarrow \{+,-\}\). Let S has q edges and \({\mathcal {A}} = \{0,1,2,\ldots , \lceil \frac{q}{2}\rceil \}\). A vertex labeling \(f:V(S)\longrightarrow {\mathcal {A}}\) which is onto, is said to be a vertex equitable labeling of S if it induces a bijective edge labeling \(f^*:E(S)\longrightarrow \{1,2,\ldots ,{\mathfrak {m}},-1,-2,\ldots ,-{\mathfrak {n}}\}\) defined by \(f^*(uv) = \sigma (uv)(f(u)+f(v))\) such that \(|v_f(a)-v_f(b)|\le 1\), \(\forall a, b\in {\mathcal {A}}\), where \(v_f(a)\) is the number of vertices with \(f(v) = a\) and \({\mathfrak {m}}, {\mathfrak {n}}\) are number of positive and negative edges respectively in S. A signed graph S is said to be vertex equitable if it admits a vertex equitable labeling. In this paper, we study vertex equitable behavior of signed bistars.

Keywords

Vertex equitable labeling Vertex equitable signed graph Bistar 

References

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    Acharya M, Jain R, Kansal S (2017) Vertex equitable labeling of signed graphs. Electron Notes Discret Math 63:461–468MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The National Academy of Sciences, India 2018

Authors and Affiliations

  1. 1.Department of Applied SciencesKIET Group of InstitutionsGhaziabadIndia
  2. 2.Department of Applied MathematicsDelhi Technological UniversityDelhiIndia
  3. 3.Department of MathematicsKalasalingam UniversityKrishnanKoilIndia

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