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Mahesh Parahar has Published 255 Articles
Mahesh Parahar
2K+ Views
Trees are graphs that do not contain even a single cycle. They represent hierarchical structure in a graphical form. Trees belong to the simplest class of graphs. Despite their simplicity, they have a rich structure.Trees provide a range of useful applications as simple as a family tree to as complex ... Read More
Mahesh Parahar
468 Views
Two functions f: A → B and g: B → C can be composed to give a composition g o f. This is a function from A to C defined by (g o f)(x) = g(f(x))ExampleLet f(x) = x + 2 and g(x) = 2x + 1, find (f o ... Read More
Mahesh Parahar
3K+ Views
The rules of mathematical logic specify methods of reasoning mathematical statements. Greek philosopher, Aristotle, was the pioneer of logical reasoning. Logical reasoning provides the theoretical base for many areas of mathematics and consequently computer science. It has many practical applications in computer science like design of computing machines, artificial intelligence, ... Read More
Mahesh Parahar
2K+ Views
Let 'G−' be a simple graph with some vertices as that of 'G' and an edge {U, V} is present in 'G−', if the edge is not present in G. It means, two vertices are adjacent in 'G−' if the two vertices are not adjacent in G.If the edges that ... Read More
Mahesh Parahar
569 Views
Graph coloring is nothing but a simple way of labelling graph components such as vertices, edges, and regions under some constraints. In a graph, no two adjacent vertices, adjacent edges, or adjacent regions are colored with minimum number of colors. This number is called the chromatic number and the graph ... Read More
Mahesh Parahar
666 Views
Let 'G' be a connected graph with 'n' vertices and 'm' edges. A spanning tree 'T' of G contains (n-1) edges.Therefore, the number of edges you need to delete from 'G' in order to get a spanning tree = m-(n-1), which is called the circuit rank of G.This formula is ... Read More
Mahesh Parahar
3K+ Views
Injective / One-to-one functionA function $f: A \rightarrow B$ is injective or one-to-one function if for every $b \in B$, there exists at most one $a \in A$ such that $f(s) = t$.This means a function f is injective if $a_1 e a_2$ implies $f(a1) e f(a2)$.Example$f: N \rightarrow N, ... Read More
Mahesh Parahar
3K+ Views
The center of a tree is a vertex with minimal eccentricity. The eccentricity of a vertex X in a tree G is the maximum distance between the vertex X and any other vertex of the tree. The maximum eccentricity is the tree diameter. If a tree has only one center, ... Read More
Mahesh Parahar
2K+ Views
Graph traversal is the problem of visiting all the vertices of a graph in some systematic order. There are mainly two ways to traverse a graph.Breadth First SearchDepth First SearchBreadth First Search (BFS) starts at starting level-0 vertex X of the graph G. Then we visit all the vertices that ... Read More
Mahesh Parahar
6K+ Views
Bipartite Graph - If the vertex-set of a graph G can be split into two disjoint sets, V1 and V2 , in such a way that each edge in the graph joins a vertex in V1 to a vertex in V2 , and there are no edges in G that ... Read More
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