A Study on Some Eccentricity Related Problems in Graphs

Title

A Study on Some Eccentricity Related Problems in Graphs

Creator

Rohith, Raja M

Contributor

Rajashekar, Paradesi Tabitha

Description

The concepts related to eccentricity in graphs are explored in this research work. newlineThe eccentric graph Ge of a graph G has the same vertex set as that of G and two newlinevertices in Ge are adjacent if one is the eccentric vertex of the other. The eccentric newlinegraphs of some graph operations are explored, and the iterated eccentric graphs Gek newlineare introduced. The process of inding eccentric graphs, known as eccentrication, is newlinestudied in detail. Graphs that result in a complete graph Kn upon iterative eccentrication are characterized, and the cyclic property of eccentrication is established for various cycle-related graphs. The eccentrication of tree graphs is studied in detail, and a general result on the cyclic property of trees is obtained. A conjecture on the cyclic property of eccentrication for any graph G is made. The ei-signed graph of a graph G, where the edge between vertices u and v receives a sign and#963; = (and#8722;1)|ecc(u)and#8722;ecc(v)|, where ecc(u) is the eccentricity of vertex u, is investigated. General properties of ei-signed graphs, such as homogeneity, consistency, switching, and sign compatibility, are discussed. Properties that behave diferently across various classes of graphs are explored. Finally, the scope of this study is presented, and some open problems in the area are provided.

Source

Author's Submission

Date

2024-01-01

Publisher

Christ(Deemed to be University)

Subject

Mathematics and Statistics

Rights

Open Access

Relation

61000301

Format

PDF

Language

English

Type

PhD

Identifier

http://hdl.handle.net/10603/545539