Square Signed Graph

  • Deepa SinhaEmail author
  • Deepakshi Sharma
Short Communication


The square graph \(G^2\) of a graph \(G=(V,E)\) is a graph with same vertex set as G, and the vertices are adjacent in \(G^2\) when their distance in G is at most two. In this paper, we characterize signed graph (or sigraph) which is a square root signed graph of some signed graph. Also, we find whether for a given signed graph its square signed graph and line of square signed graph are balanced. Each theorem is supported by respective algorithms.


Square signed graph Balance signed graph Line signed graph Algorithm 



Funding was provided by South Asian University.


  1. 1.
    Acharya M (2009) Line signed graphs. J Comb Math Comb Comput 69:103–111MathSciNetzbMATHGoogle Scholar
  2. 2.
    Chartrand G, Behzad M (1969) Line-coloring of signed graphs. Elemente der Mathematik 24:49–52MathSciNetzbMATHGoogle Scholar
  3. 3.
    Gill MK, Patwardhan GA (1981) A characterization of sigraphs which are switching equivalent to their line sigraphs. J Math Phys Sci 15(6):567–571MathSciNetzbMATHGoogle Scholar
  4. 4.
    Harary F (1969) Graph theory. Addision Wesley, ReadingCrossRefGoogle Scholar
  5. 5.
    Harary F, Kabell JA (1980) A simple algorithm to detect balance in signed graphs. Math Soc Sci 1(1):131–136MathSciNetCrossRefGoogle Scholar
  6. 6.
    Mukhopadhyay A (1967) The square root of a graph. J Comb Theory 2(3):290–295MathSciNetCrossRefGoogle Scholar
  7. 7.
    Sinha D, Sharma D (2016) On square and 2-path signed graph. J Interconnect Netw 16(01):1550011CrossRefGoogle Scholar
  8. 8.
    Sinha D, Sharma D (2018) On the properties of square signed graph. Natl Acad Sci Lett 41(4):233–238MathSciNetCrossRefGoogle Scholar
  9. 9.
    West DB (2001) Introduction to graph theory, vol 2. Prentice Hall, Upper Saddle RiverGoogle Scholar
  10. 10.
    Zaslavsky T (1998) Signed analogs of bipartite graphs. Discrete Math 179(1):205–216MathSciNetCrossRefGoogle Scholar
  11. 11.
    Zaslavsky T (2012) A mathematical bibliography of signed and gain graphs and allied areas. Electron J Comb 1000, DS8-SepGoogle Scholar

Copyright information

© The National Academy of Sciences, India 2019

Authors and Affiliations

  1. 1.Department of MathematicsSouth Asian UniversityNew DelhiIndia
  2. 2.Department of MathematicsRamanujan College, University of DelhiNew DelhiIndia

Personalised recommendations