The graph coloring problem is an optimization problem involving the assignment of one of q
colors to each vertex of a graph such that no two adjacent vertices share the same color …

In this thesis we study reconfiguration problems in graph theory. A reconfiguration problem
is generally defined on the solution space of a problem for which a configuration can be …

For a commutative ring R, even elements in R as vertices and two distinct vertices xi, yj∈ R
are adjacent iff xiyj= 0 or yjxi= 0, then the graph is known as an even prime graph. In …

Abstract Let M=\{1, 2,.. m\} and G be a simple graph. A graceful m-coloring of G is a proper
vertex coloring of G using the colors in M which leads to a proper edge coloring using …

Graph Theory is a very complex and difficult mathematical problem, with Graph Coloring as
one of its most studied problem. Graph Coloring itself is an implementation of Graph Theory …

2-odd labeling assigns distinct integers to the nodes of a graph G (V, E) in such a manner,
that the positive difference of adjacent nodes is either 2 or an odd integer, 2k±1, k? N. So, G …

In graph coloring, labels are assigned to graph elements according to certain constraints.
Colors are a special case of graph labeling as well as in practical applications, graph …

Over the past decades, there has been a lot of studies on graphs associated to groups which
are significant in providing effective formulation on the characteristics of the algebraic …

The necessity for good and tenable communication systems has motivated researchers to
develop mobile communication networks (MCN). On the other hand, the huge functionalities …

Graph theory plays a significant role in a variety of real-world systems. Graph concepts such
as labeling and coloring are used to depict a variety of processes and relationships in …