 Hello and welcome to the session. In this session we will discuss graph terminology i.e. we will discuss definition of graph and basic terms related to graphs. First of all we shall discuss what is a graph? A graph consists of points called vertices or nodes which are connected by lines known as edges or arcs. Now see this graph which connects the three points a, b and c called vertices and edges are represented as lines joining vertices. Now we are going to discuss directed graphs and undirected graphs. In our graph we can move from one vertex to the other vertex if the two vertices are connected by a line and if we can move in either direction along the line then the lines are called edges and the graph is an undirected graph. Now see in this graph a, b and c are connected by lines so we can move from vertex a to vertex b. Similarly we can also move from vertex b to vertex a. If we see vertices a and c then we can either move from vertex a to vertex c or from vertex c to vertex a so it is an undirected graph and the lines connecting vertices are the edges. Now let us put our direction sign on these lines. Now if we study this graph the arrow tells us the direction in which we can move from one vertex to the other. See here we can move from vertex a to vertex b but we cannot move from vertex b to vertex a. So in this graph we can move from vertex a to vertex b from vertex b to vertex c and from vertex c to vertex a thus it is a directed graph or we can also call it as digraph and the lines connecting the vertices are called arcs. Now we are going to learn about degree of a vertex. Degree of a vertex is the number of edges or arcs that touch a vertex. Now if we consider this given graph we see that it is having one, two, three, four that is four vertices or nodes and these are a, b, c and d. Now let us find the degree of each vertex c number of edges which touch vertex a are one, two that is two. So degree of vertex a is two. Similarly degree of vertex b will be equal to one, two that is two. Now degree of vertex c is one, two, three that is three because there are three edges which touch vertex c and degree of vertex d will be equal to one because only one edge touches it. So here we have degree of vertex a is two, degree of vertex b is two, degree of vertex c is three and degree of vertex d is one. Now we are going to see what is a loop. A loop is an edge that starts and ends at the same vertex. It contributes two to the degree of vertex. Now in this graph there are two vertices a and b. We can see there is a loop at vertex a that is from a to a. Let us see degree of the vertices a and b. Since loop contributes two to the degree of vertex a, so degree of vertex a will be three and degree of vertex b is one. Now we are going to discuss path. A path is a finite sequence of edges such that the end vertex of one edge in the sequence is the start vertex of the second and in which no vertex appears more than once. Now see in this graph we can find the following paths to reach vertex d. One path can be from vertex a to vertex b from vertex b to vertex c and then to vertex d. The other path can be from vertex a to vertex c and then to vertex d. Next we have circuit. A circuit is a path that starts and ends at the same vertex. Now see in this graph we can start from vertex a and finish at vertex a by following the path from vertex a to vertex b to vertex c and then to vertex a. So this path is a circuit. Now we are going to discuss connected and disconnected graphs. A graph is course connected if all its vertices are connected and a path can be found between any two vertices. Now if we look at this graph we can say that this is a connected graph because we can move from one vertex to the other vertex by following edges. See a path is found between any two vertices. If we want to move from vertex b to vertex d we can follow the path from vertex b to vertex c and then to vertex d. Now a graph is called disconnected if all its vertices are not connected. See this is a disconnected graph as we cannot find the path from vertex b to vertex d. Now we are going to discuss simple graph. A simple graph is a graph in which there are no loops and not more than one edge connecting any pair of vertices. This is a simple graph because there is only one edge between any pair of vertices and there are no loops. Now if we see this graph we can say that it is not a simple graph because there are two edges connecting vertices a and c. Now we are going to discuss about complete graph. A complete graph is a graph in which every vertex is directly connected by an edge to each of the other vertices. See this is a complete graph because each vertex is connected with all the other vertices by edges. See vertex a is connected to vertex b, vertex c and vertex d. Similarly vertex b is connected to vertex a, vertex c and vertex d by edges. Now this is an incomplete graph because vertex b is not connected to vertex c by an edge. Thus in this session we have discussed definition of graph and basic terms related to graphs. This completes our session. Hope you enjoyed this session.