In the thesis, we mainly discuss variants of two well-studied graph theoretical problems - vertex deletion problem and graph coloring problem - both have been used to tackle many real-world problems in diverse fields. Vertex ...

The boxicity of a graph G, denoted as box(G), is the minimum dimension d for which each vertex of G can be mapped to a d-dimensional axis-parallel box in Rd such that two boxes intersect if and only if the corresponding ...

The discrete k-watchtower problem for a polyhedral terrain T in R3 with n vertices is to nd k vertical segments, called watchtowers, of smallest height, whose bottom end-points (bases) lie on some vertices of T, and ...

The anti-Ramsey number ar(G,H) with input graph G and pattern graph H, is the maximum positive integer k such that there exists an edge coloring of G using k colors, in which there are no rainbow subgraphs isomorphic to ...

In this thesis we study the isoperimetric problem on trees and graphs with bounded treewidth. Let G = (V,E) be a finite, simple and undirected graph. For let δ(S,G)= {(u,v) ε E : u ε S and v ε V – S }be the edge boundary ...

The classical graph edge coloring problem deals in coloring the edges of a given graph with minimum number of colors such that no two adjacent edges in the graph, get the same color in the proposed coloring. In the following ...

This thesis touches three different topics in graph theory, namely, rainbow colouring, product dimension and boxicity. Rainbow colouring An edge colouring of a graph is called a rainbow colouring, if every pair of vertices ...