The number of processor cores and on-chip cache size has been increasing on chip multiprocessors (CMPs). As a result, leakage power dissipated in the on-chip cache has become very significant. We explore various techniques ...

A proper edge coloring of G =(V,E)is a map c : E → C (where C is the set of available colors ) with c(e) ≠ c(ƒ) for any adjacent edges e,f. The minimum number of colors needed to properly color the edges of G, is called ...

Let F be a family of sets. A graph G is an intersection graph of sets from the family F if there exists a mapping f : V (G)→ F such that, An interval graph is an intersection graph of a family of closed intervals on the ...

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 ...

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 ...

In this thesis we study the following dimensional parameters : boxicity, cubicity, threshold dimension and poset dimension. While the first three parameters are defined on graphs, poset dimension is defined on partially ...

A graph Gis said to be an intersection graph of sets from a family of sets if there exists a function ƒ : V(G)→ such that for u,v V(G), (u,v) E(G) ƒ (u) ƒ (v) ≠ . Interval graphs are thus the intersection graphs ...

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 ...

The minimum number of colors required to color the edges of a graph so that any two distinct vertices are connected by at least one path in which no two edges are colored the same is called its rainbow connection number. ...

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 ...