Answer :
The maximum number of edges in a directed graph without any self-loops, having a total 6 of vertices is 15.
Edge:
In geometry, an edge is a particular type of line segment that connects two vertices of a polygon, polyhedron, or higher-dimensional polyhedron. In polygons, edges are line segments of the boundary and are often called polygon sides. In a polyhedron, or more generally a polytope, an edge is a line segment where two faces (or sides of a polyhedron) meet. A line segment connecting two vertices and passing inside or outside is called a diagonal, not an edge.
Directed graph:
A directed graph is a graph. A series of objects (called nodes or knots) connected together with all edges pointing from one node to another. A directed graph is sometimes called a directed graph or directed network. In contrast, graphs whose edges are bidirectional are called undirected graphs.
The graph containing maximum number of edge in a n node undirected graph without self loop is complete graph.
The number of edges in complete graph with n node, kₙ is
n(n − 1)/ 2
Now, based on the above formula:
n( n -1) /2
= 6( 6 - 1)/2
= 5× 6/2 = 30/2 = 15
Therefore, The maximum number of edges in a directed graph without any self-loops, having a total 6 of vertices is 15.
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