A compilation of various topic from graph theory containing problem from various platform like https://codeforces.com/, https://www.spoj.com/, https://www.codechef.com/, https://www.hackerrank.com/, etc.
The topics may be referred from here: https://www.hackerearth.com/practice/algorithms/graphs/graph-representation/tutorial/ and Graph section of https://cp-algorithms.com/.
The history of graph theory may be specifically traced to 1735, when the Swiss mathematician Leonhard Euler solved the Königsberg bridge problem.
Graph theory, branch of mathematics concerned with networks of points connected by lines. The subject of graph theory had its beginnings in recreational math problems, but it has grown into a significant area of mathematical research, with applications in chemistry, operations research, social sciences, and computer science.