Topological Indices Based on Distance Labeling

Title

Topological Indices Based on Distance Labeling

Creator

Raj, Anna Treesa

Contributor

Varghese, Joseph.

Description

This thesis explores the prospect of combining two prime branches of graph theory, newlineviz., topological indices and graph labeling, specifcally radio labeling. The majority newlineof the work includes the topological radio indices of graphs and their properties. Topological indices are numerical values associated with graphs and invariant with graph isomorphisms. Apart from Topological Radio Indices, it provides some additions to the eccentricity-based topological indices. newlineRadio labeling or radio coloring, c, is assigned to a graph G such that the label difference between any two vertices must be greater than diam(G)+ 1 and#8722; d(u,v). Optimum radio labeling is the foundation for defning Topological radio indices. Labeling whose span is the radio number of the graph and which leads to the minimum value of the index newlineis considered the optimum radio labeling. The topological radio indices and coindices newlineare defned and are found out for some special classes of graphs, including gear graphs, newlinewheel graphs, and star graphs. The bounds for the frst, second and third Zagreb radio indices have been established and characterized for the classes of graphs for which the bound is sharp. Furthermore, newlinespecifc relationships between Zagreb radio indices and coindices are established concerning different parameters of the graph. newlineThe idea of consecutive radio labeling is explicitly studied. We have characterized the newlinegraphs with diameter 2 admitting consecutive radio labeling. We have studied the properties of graphs admitting consecutive radio labeling and stated the necessary and suffcient conditions for a graph to follow consecutive radio labeling. The study extended to eccentricity-based topological indices, viz., the forgotten eccentricity indices. The maximum d(u,v) for all v in V(G) is the eccentricity of the vertex u in G. This work also investigates eccentricity-based coindices and some of their properties. newlineApart from this, some uniquely radio colorable graphs are examined and characterized.

Source

Author's Submission

Date

2023-01-01

Publisher

Christ(Deemed to be University)

Subject

Mathematics and Statistics

Rights

Open Access

Relation

61000240

Format

PDF

Language

English

Type

PhD

Identifier

http://hdl.handle.net/10603/501733