Instructor Profile:
Dr. Pankaj Dashore
Professor, School of Computer Science & Engineering (SOCSE), Sandip University, Nashik
Dr. Pankaj Dashore is a distinguished academician and researcher with over 26 years of experience in the field of Computer Science & Engineering. He holds a Ph.D. in Computer Engineering and an M.Tech in Computer Science from the Institute of Engineering and Technology, Devi Ahilya Vishwavidyalaya, Indore. Dr.Dashore has made significant contributions to the academic and research community, having published more than 50 papers in reputed peer-reviewed journals. Additionally, he has authored three books, one of which was published by IGI Global, an international academic publisher, in 2024.
Throughout his career, Dr.Dashore has demonstrated strong leadership, holding key positions at renowned institutions. He served as the Principal of Sanghvi Institute of Management and Science, Indore, from 2016 to 2022, and later as Head of Institute (ICA) at Sage University, Indore, from 2022 to 2023. Currently, he is a professor at Sandip University, Nashik, where he continues to contribute to both academia and research.
Dr.Dashore’s academic contributions extend to intellectual property, with two copyrights and five patent publications. He is also an active member of several prestigious professional organizations, including IETE (Fellow), IEEE (Senior Member), ACM, and CSI. His commitment to research and technological innovation was recognized in 2023 when he was awarded the “Innovative Technological Research & Dedicated Principal Award” at the International Education Award Ceremony.
In addition to his academic and leadership roles, Dr.Dashore has been instrumental in organizing national and international conferences, securing grants from prominent bodies such as MPCST and BRNS in 2013. His ongoing dedication to fostering innovation in technology and excellence in education makes him a highly respected figure in the field.
Course Outline: Hamiltonian, Euler’s Circuit, and Graph Coloring
This course provides an in-depth understanding of fundamental concepts in graph theory, focusing on Hamiltonian circuits, Euler’s circuits, and graph coloring. It is structured into four comprehensive modules designed to build foundational knowledge and practical application skills.
Module 1: Introduction to Graph Theory and Euler’s Circuit
- Basic Concepts of Graph Theory: Definitions: Graphs, vertices, edges, degree, paths, and circuits, Types of graphs: Directed, undirected, weighted, unweighted, Applications of graph theory in real-world problems
- Euler’s Circuit: Definitions: Eulerian paths and Eulerian circuits, Euler’s Theorem: Conditions for the existence of Eulerian circuits, Algorithm for finding Eulerian paths and circuits, Applications of Euler’s circuit (e.g., route planning, network analysis)
Module 2: Hamiltonian Circuit and Related Concepts
- Hamiltonian Paths and Circuits: Definitions: Hamiltonian paths, Hamiltonian circuits, and cycles, Necessary and sufficient conditions for Hamiltonian circuits, Key theorems (e.g., Dirac’s and Ore’s Theorems), Examples and practical applications of Hamiltonian circuits in optimization problems
- Algorithms for Hamiltonian Circuits: Backtracking approach, Heuristic methods and approximation algorithms, Real-world applications: Traveling Salesman Problem (TSP)
Module 3: Graph Coloring and Chromatic Number
- Introduction to Graph Coloring: Definition: Graph coloring, chromatic number, and chromatic polynomial, Importance and applications in scheduling, resource allocation, and map coloring, Types of graph coloring: Vertex coloring, edge coloring, and face coloring
- The Four-Color Theorem: Historical background and statement of the theorem, Proof outline and its implications for planar graphs, Application in practical scenarios: Frequency assignment and circuit design
- Algorithms for Graph Coloring: Greedy coloring algorithm, Backtracking and heuristic approaches
Module 4: Advanced Applications and Problem-Solving
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- Advanced Problem-Solving in Euler’s and Hamiltonian Circuits: Complex graph analysis: Application in network design and logistics, Case studies of Eulerian and Hamiltonian circuit problems, Challenges and open problems in the field
- Advanced Graph Coloring Techniques: Optimization of graph coloring for large and complex networks, Multi-graph and hypergraph coloring, Practical problems and solutions in scheduling, partitioning, and frequency allocation
Course Outcome:
By the end of the course, learners will gain a thorough understanding of graph theory, including Eulerian and Hamiltonian circuits, and graph coloring techniques. They will be equipped with problem-solving skills applicable to real-world scenarios in computer science, optimization, and network analysis.
