#### Graph Theory

Graph Theory:

Graph theory, in computer science and mathematics is the study of graphs, which are mathematical structures utilized to model pair-wise relations among objects from a certain collection. In this context a "graph" is a collection of "vertices" or "nodes" and a collection of edges that connect pairs of vertices. A graph might be undirected, meaning that there is no distinction among the two vertices linked with each edge, or its edges might be directed from one vertex to another; see graph (mathematics) for more thorough definitions and for other variations in the types of graph that are considered commonly. Graphs are one of the key objects of study in discrete mathematics.

A graph is an ordered pair G = (V, E) in which:

• V is the vertex set whose elements are the vertices, or nodes of the graph. This set is frequently denoted as V (G) or just V.
• E is the edge set which elements are the edges, or connections among vertices, of the graph. This set is frequently denoted E (G) or just E. If the graph is undirected, particular edges are unordered pairs {u, v} where u and v are vertices in V. If the graph is directed, edges are ordered pairs (u, v).

Two graphs G and H are assume equal when V (G) = V(H) and E(G) = E(H).

The order of a graph the number of vertices in it, usually indicated by |V| or sometimes n. The size of graph is the number of edges present in it, mentioned by |E| , or sometimes m . If n = 0 or m = 0, the graph is called empty or null. If n = 1 the graph is considered trivial.

Undirected graph:

It is one where edges have no orientation. The edge (a, b) is identical to the edge (b, a),that means as they are not ordered pairs, but sets {u, v} (or 2-multisets) of vertices.

Directed graph:

A directed graph or digraph is an ordered pair D = (V, A) with following

• ‘V’ a set whose elements are called as vertices or nodes, and
• ‘A’ a set of ordered pairs of vertices, called as arcs, directed edges, or arrows.

An arc a = (x, y) is assumed to be directed from x to y; y is said the head and x is said the tail of the arc; y is called to be a direct successor of x, and x is refer to be a direct predecessor of y. If any path leads from x to y, then y is called to be a successor of x and accessible from x, and x is said to be a predecessor of y. The arc (y, x) is said the arc (x, y) inverted.

A directed graph D is said symmetric if, for each arc in D, the corresponding inverted arc also connected to D. A symmetric loop-less directed graph D = (V, A) is corresponding to a simple undirected graph G = (V, E), where the pairs of inverse arcs in A correspond 1-to-1 along with the edges in E; thus the edges in G number |E| = |A|/2, or half the number of arcs in D.

On this definition a variation is the oriented graph, in which not more than one of (x, y) and (y, x) can be arcs.

Latest technology based Computer Science Online Tutoring Assistance

Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Graph Theory homework help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Graph Theory, project ideas and tutorials. We provide email based Graph Theory homework help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Graph Theory. ThroughOnline Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobeare committed to provide the best quality online tutoring assistance for compter science and assignment help services. They use their experience, as they have solved thousands of the Computer assignments, which may help you to solve your complex issues of Graph Theory. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework helpas per the deadline or given instruction by the student, we refund the money of the student without any delay.