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UNIVERSITY OF KERALA - Marian Engineering College

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B.Tech Comp. Sc. & Engg., University of Kerala 82<br />

08.805 (4) GRAPH THEORY (ELECTIVE III) 3 – 1 – 0<br />

(Common with F 08.805C)<br />

Module I (16 hours)<br />

What is graph – Application of graphs – finite and infinite graphs – Incidence and Degree – Isolated vertex,<br />

pendent vertex, Null graph.<br />

Paths and circuits – Isomorphism, sub graphs, walks, paths and circuits, Connected graphs, disconnect graphs,<br />

Euler graphs Hamiltonian paths and circuits – Travelling salesman problem.<br />

Trees – properties, pendent vertex, Distance and centres - Rooted and binary tree, counting trees, spanning<br />

trees.<br />

Module II (18 hours)<br />

Combinatorial versus geometric graphs, Planar graphs, Different representation of planar graphs, geometric<br />

dual, combinatorial dual, vector spaces of graph, ban2 vectors of a graph, orthogonal vectors and spaces<br />

Directed graphs – types of digraphs, Digraphs and binary relation, Euler graphs, trees with directed edges.<br />

Module III (18 hours)<br />

Graphs theoretic algorithms and computer programming - Algorithm for computer representation of a graph,<br />

algorithm for connectedness and components, spanning tree, directed circuits, shortest path, searching the<br />

graphs, Isomorphism.<br />

Graphs in switching and cording theory – contact networks, Analysis of contact Networks, synthesis of<br />

contact networks, sequential switching networks, unit cube and its graph, graphs in coding theory.<br />

Text Books:<br />

1. Graph theory – Hararay, Narosa Publishers<br />

2. Graph theory – Narasingh Deo, PHI.<br />

Reference Books:<br />

1. Graphs theory applications – L.R. Foulds, Narosa.<br />

2. A first look at graph theory – John clark and Derek Allan Hotton, Allied.<br />

Internal Continuous Assessment (Maximum Marks-50)<br />

25 Marks - Tests (minimum 2)<br />

15 Marks - Assignments (minimum 3) such as home work, problem solving, literature survey, seminar,<br />

term-project, software exercises, etc.<br />

10 Marks - Regularity in the class<br />

University Examination Pattern<br />

PART A: Short answer questions 10 x 4 marks=40 marks<br />

All questions are compulsory. There should be at least three questions<br />

from each module and not more than four questions from any module.<br />

PART B: Descriptive/Analytical/Problem solving questions 3 x 20 marks=60 marks<br />

Candidates have to answer one question out of two or two questions<br />

out of four from each module<br />

Maximum Total Marks: 100

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