ON BLOCK-RELATED DERIVED GRAPHS

Title

ON BLOCK-RELATED DERIVED GRAPHS

Creator

Baskar N.; Mangam T.A.; Rohith Raja M.

Description

This paper introduces and analyses the block-degree of a vertex and the cut-degree of a block. The block-degree of a vertex v is the number of blocks containing v. The cut-degree of a block b is the number of cut vertices of G contained in b. The block-degree sequence of cut vertices of the graph and the cut-degree sequence of the graph are defined. A few characterizations of the block-degree and cut-degree sequence of the graph are established. Given a graph, its block graph (B(G)) is a graph where each vertex represents a block, and two vertices are connected if their blocks intersect. The number of cut vertices of B(G) is determined. Further, an investigation is carried out on the traversability of B(G). A block cutpoint graph (BC(G)) of a graph represents a graph where each vertex corresponds to either a block or a cut vertex, and two vertices are connected if one represents a block and the other represents a cut vertex contained within that block. The properties of BC(G) and its iterations are studied. The graph G for which BC(G) is a perfect m-ary tree is characterized. 2024, Canadian University of Dubai. All rights reserved.

Source

Gulf Journal of Mathematics, Vol-18, No. 2, pp. 70-86.

Date

2024-01-01

Publisher

Canadian University of Dubai

Subject

block cut point graph of a graph; block graph of a graph; block-degree; cut-degree

Coverage

Baskar N., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India; Mangam T.A., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India; Rohith Raja M., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India

Rights

All Open Access; Hybrid Gold Open Access

Relation

ISSN: 23094966

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.56947/gjom.v18i2.2284

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