Graph Theory By Narsingh Deo Exercise Solution – Direct

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Focus: Determining planarity, Euler’s formula, and Kuratowski’s Theorem.

Theorem: Euler’s Formula For a connected planar graph: $v - e + f = 2$ (Where $v$ = vertices, $e$ = edges, $f$ = faces/regions).

Sample Problem: Question: A connected planar graph has 6 vertices and 10 edges. How many regions does it have? Solution: Graph Theory By Narsingh Deo Exercise Solution

Kuratowski’s Theorem: Exercises often ask to prove a graph is non-planar.

Unlike many modern textbooks that include only computational problems, Deo’s book emphasizes:

The exercises range from routine to research-level difficulty. Chapters on Planar Graphs, Graph Colorings, and Directed Graphs contain problems that test deep theoretical understanding, not just memorization. While searching for "Graph Theory By Narsingh Deo

Focus: Connectivity, Euler paths, and Hamiltonian circuits.

Common Exercise Type: Determining if a graph is Eulerian or Hamiltonian.

Sample Problem: Question: A connected graph has exactly two vertices of odd degree. Prove it contains an Euler path. Kuratowski’s Theorem: Exercises often ask to prove a

Solution Approach:

Algorithmic Application: Many exercises in this chapter require the application of the Fleury’s Algorithm to find an Euler circuit or the Nearest Neighbor Method (heuristic) for the Traveling Salesman Problem (Hamiltonian circuit).