On C-Perfection of Tensor Product of Graphs

Title

On C-Perfection of Tensor Product of Graphs

Creator

Jayakumar G.S.; Sangeetha V.

Description

A graph G is C-perfect if, for each induced subgraph H in G, the induced cycle independence number of H is equal to its induced cycle covering number. Here, the induced cycle independence number of a graph G is the cardinality of the largest vertex subset of G, whose elements do not share a common induced cycle, and induced cycle covering number is the minimum number of induced cycles in G that covers the vertex set of G. C-perfect graphs are characterized as series-parallel graphs that do not contain any induced subdivisions of K2,3, in literature. They are also isomorphic to the class of graphs that has an IC-tree. In this article, we examine the C-perfection of tensor product of graphs, also called direct product or Kronecker product. The structural properties of C-perfect tensor product of graphs are studied. Further, a characterization for C-perfect tensor product of graphs is obtained. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

Source

Lecture Notes in Networks and Systems, Vol-865, pp. 235-249.

Date

2024-01-01

Publisher

Springer Science and Business Media Deutschland GmbH

Subject

C-perfect graphs; Graph minors; Perfect graphs; Product graphs; Tensor product

Coverage

Jayakumar G.S., CHRIST (Deemed to be University), Karnataka, Bangalore, 560029, India; Sangeetha V., CHRIST (Deemed to be University), Karnataka, Bangalore, 560029, India

Rights

Restricted Access

Relation

ISSN: 23673370; ISBN: 978-981999042-9

Format

Online

Language

English

Type

Conference paper

Identifier

https://doi.org/10.1007/978-981-99-9043-6_20

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85190389132&doi=10.1007%2f978-981-99-9043-6_20&partnerID=40&md5=3c934868d2e78f4df4a19a70539532a6