Non-inverse signed graph of a group

Title

Non-inverse signed graph of a group

Creator

Amreen J.; Naduvath S.

Description

Let G be a group with binary operation *. The non-inverse graph (in short, i*-graph) of G, denoted by ?, is a simple graph with vertex set consisting of elements of G and two vertices x, y ? ? are adjacent if x and y are not inverses of each other. That is, x ? y if and only if x * y ?= iG ?= y*x, where iG is the identity element of G. In this paper, we extend the study of i*-graphs to signed graphs by defining i*-signed graphs. We characterize the graphs for which the i*-signed graphs and negated i*-signed graphs are balanced, sign-compatible, consistent and k-clusterable. We also obtain the frustration index of the i*-signed graph. Further, we characterize the homogeneous non-inverse signed graphs and study the properties like net-regularity and switching equivalence. Amreen J., Naduvath S., 2024.

Source

Carpathian Mathematical Publications, Vol-16, No. 2, pp. 565-574.

Date

2024-01-01

Publisher

Precarpathian National University

Subject

algebraic graph; non-inverse graph; non-inverse signed graph

Coverage

Amreen J., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, India; Naduvath S., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, India

Rights

All Open Access; Gold Open Access

Relation

ISSN: 20759827

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.15330/cmp.16.2.565-574

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