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Line and Subdivision Graphs Determined by T 4 -Gain Graphs

Author

Listed:
  • Abdullah Alazemi

    (Department of Mathematics, Kuwait University, Safat 13060, Kuwait)

  • Milica Anđelić

    (Department of Mathematics, Kuwait University, Safat 13060, Kuwait)

  • Francesco Belardo

    (Department of Mathematics and Applications, University of Naples, 80138 Napoli, Italy)

  • Maurizio Brunetti

    (Department of Mathematics and Applications, University of Naples, 80138 Napoli, Italy)

  • Carlos M. da Fonseca

    (Kuwait College of Science and Technology, Doha District, Block 4, P.O. Box 27235, Safat 13133, Kuwait
    University of Primorska, FAMNIT, Glagoljsaška 8, 6000 Koper, Slovenia)

Abstract

Let T 4 = { ± 1 , ± i } be the subgroup of fourth roots of unity inside T , the multiplicative group of complex units. For a T 4 -gain graph Φ = ( Γ , T 4 , φ ) , we introduce gain functions on its line graph L ( Γ ) and on its subdivision graph S ( Γ ) . The corresponding gain graphs L ( Φ ) and S ( Φ ) are defined up to switching equivalence and generalize the analogous constructions for signed graphs. We discuss some spectral properties of these graphs and in particular we establish the relationship between the Laplacian characteristic polynomial of a gain graph Φ , and the adjacency characteristic polynomials of L ( Φ ) and S ( Φ ) . A suitably defined incidence matrix for T 4 -gain graphs plays an important role in this context.

Suggested Citation

  • Abdullah Alazemi & Milica Anđelić & Francesco Belardo & Maurizio Brunetti & Carlos M. da Fonseca, 2019. "Line and Subdivision Graphs Determined by T 4 -Gain Graphs," Mathematics, MDPI, vol. 7(10), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:926-:d:273733
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