Line and Subdivision Graphs Determined by T 4 -Gain Graphs

Abdullah Alazemi, Milica Anđelić, Francesco Belardo, Maurizio Brunetti and Carlos M. da Fonseca
Additional contact information
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

Mathematics, 2019, vol. 7, issue 10, 1-12

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.

Keywords: complex unit gain graph; line graph; subdivision graph; oriented gain graph; voltage graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/10/926/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/10/926/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:10:p:926-:d:273733

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().