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#### Algorithmic and Combinatorial Questions on Some Geometric Problems on Graphs

(2018-05-08)

This thesis mainly focuses on algorithmic and combinatorial questions related to some geometric problems on graphs. In the last part of this thesis, a graph coloring problem is also discussed.
Boxicity and Cubicity: These ...

#### Game-Theoretic Analysis of Strategic Behaviour in Networks, Crowds and Classrooms

(2018-01-03)

Over the past decade, the explosive growth of the Internet has led to a surge of interest to understand and predict aggregate behavior of large number of people or agents, particularly when they are connected through an ...

#### Acyclic Edge Coloring Of Graphs

(2013-10-07)

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 ...

#### Rainbow Colouring and Some Dimensional Problems in Graph Theory

(2018-04-05)

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 ...

#### On Dimensional Parameters Of Graphs And Posets

(2013-06-21)

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 ...

#### Parameterized Complexity of Maximum Edge Coloring in Graphs

(2018-03-09)

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 ...

#### Rainbow Connection Number Of Graph Power And Graph Products

(2014-09-09)

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. ...

#### The Isoperimetric Problem On Trees And Bounded Tree Width Graphs

(2010-08-26)

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 ...

#### Hadwiger's Conjecture On Circular Arc Graphs

(2009-04-30)

Conjectured in 1943, Hadwiger’s conjecture is one of the most challenging open problems in graph theory. Hadwiger’s conjecture states that if the chromatic number of a graph G is k, then G has a clique minor of size at ...

#### New Models and Methods for Formation and Analysis of Social Networks

Social networks are an inseparable part of human lives, and play a major role in a wide range of activities in our day-to-day as well as long-term lives. The rapid growth of online social networks has enabled people to ...