Article in press
Authors:
Divya Bankapur
Department of Mathematics
Christ University, Bangalore, India
email: divyabankapur@gmail.com
Sudev Naduvath
Department of Mathematics
Christ University, Bangalore, India
email: sudevnk@gmail.com
Title:
On $L(2,1)$-order sum signed graph of a finite group
PDFSource:
Discussiones Mathematicae - General Algebra and Applications
Received: 2024-07-06 , Revised: 2024-08-30 , Accepted: 2024-08-30 , Available online: 2025-05-23 , https://doi.org/10.7151/dmgaa.1480
Abstract:
In this paper, we have constructed a color-induced signed graph of an algebraic
graph, called the L(2, 1)-order sum signed graph of a group. Based on
the nature of the group, we have obtained the L(2, 1)-span of the order sum
graph and investigated the structural aspects of thus obtained L(2, 1)-order
sum signed graph such as planarity, chordality, etc. We have also defined an
automorphism which turns out to be the only possible automorphism on the
graph and have investigated the structural aspects of the graph such as edge
transitivity and vertex transitivity. Further, we have constructed a line-signed
graph of L(2, 1)-order sum signed graph which is a line graph with a signing
protocol defined for the edges. We have investigated the regularity of the
line-signed graph. In addition to this, we have defined a homomorphism from
L(2, 1)-order sum signed graph to its line-signed graph.
Keywords:
$L(2,1)$-coloring, $L(2,1)$-order sum signed graph, signed graph homomorphism, pseudo-planarity, positive chordality, negative chordality
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arXiv: 1401.3308
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