3. а)Define the following terms as used in graph theory:i)regular graphii)simple circuit[1 1 2]b)Let A = |1 0 1 be the adjacency matrix for the graph G, with[2 1 o]vertices vi, v2, V3.i)Find the number of walks of length 2, from vi to vi.ii)Draw the graph G and label the edges e; (i= 1, 2, 3, ...)iii)Write down the walks of length 2 from vị to vi. Whichones are simple circuits?1 010 0represents the relations R defined o111 11c)The matrix M:11-the set A = {1, 2, 3, 4}.i)List the ordered pairs in the relation R.ii)Draw the graph representing the relation R.d)How many edges does a 50-regular graph with 100 vertices have? 5. а)Define the following with an example:i)Domain of a functionii)One – to – one function4х +1A function f is defined on the det of real numbers by f(x)=2х -3b)i)Write down the domain of f.ii)Show that f is a one – to – one function.iii)Find the inverse of the function f.c)Given the function f(x) = x², g(x) = 3x – 4, find the compositefunction gof (where gofmeans f followed by g)d)A function fis defined on the set N of natural numbers byA0) = 2, {2) = 5 and ſ(n) = 2 A(n - 1)+3 f(n - 2) + An - 3)for all n 2 3. Find f(4).

A graph is called a regular graph as graph it degree of each vertex. is equal. A graph is called k…

Answered: 3. а) Define the following terms as…

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3. а) Define the following terms as used in graph theory: i) regular graph ii) simple circuit

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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