Kenneth Rosen Edition 6th Exercise 8.4 Question 17 (Page No. 575)

Question

Find the number of paths of length n between two different vertices in K4 if n is
a) 2. b) 3. c) 4. d) 5.

Comments

Mathematical way of doing this : Create the adjacency matrix of K₄ ..Say this is denoted as A..Then to find no of paths of length 2 , we find A² , so A[i][j] entry of A² will give number of paths of length 2 between vertices labelled 'i' and 'j'..

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yes habib, I understand this method of finding, but my main doubt is,As there is considerable variation of terminology concerning the concepts of PATH. a path can be simply a set of vertices(distinct or repeated ), but wiki and many other resources says "A path is a trail in which all vertices (except possibly the first and last) are distinct" unlike said in rosen.now which to consider while solving problems.

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hello reena, i want to clear your doubt about HAMILTON PATH and HAMILTON CIRCUIT(CYCLE):-

HAMILTON PATH: a simple path in a graph G that passes through every vertex exactly once is called HAMILTON PATH (i.e. in hamilton path starting and last vertex should be different.) 

HAMILTON CIRCUIT(CYCLE):  a simple circuit in a graph G that passes through every vertex exactly once is called HAMILTON CIRCUIT (i.e. in hamilton circuit starting and last vertex should be same thats why it is called the circuit.)

your doubt definately will be clear from this example:-