GATE CSE 1988 | Question: 2xvi

Question

Write the adjacency matrix representation of the graph given in below figure.

Answer 1

$$\begin{array}{|c|c|c|c|c|c|} \hline \textbf{} & \textbf{$P_1$}& \textbf{$P_2$} & \textbf{$P_3$} & \textbf{$P_4$} & \textbf{$P_5$}\\\hline \textbf{$P_1$} & \text{$0$}& \text{$1$} & \text{$0$} & \text{$0$} & \text{$1$}\\\hline \textbf{$P_2$} & \text{$0$}& \text{$0$} & \text{$0$} & \text{$1$} & \text{$0$}  \\\hline \textbf{$P_3$} & \text{$1$}& \text{$0$} & \text{$0$} & \text{$0$} & \text{$0$}  \\\hline \textbf{$P_4$} & \text{$0$}& \text{$0$} & \text{$1$} & \text{$0$} & \text{$1$} \\\hline \textbf{$P_5$} & \text{$0$}& \text{$1$} & \text{$0$} & \text{$0$} & \text{$0$} \\\hline \end{array}$$

Comments

Sir can i put p1 to p1 1.p1 to p1 is also a path

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If self loop is in p1 then we can write .

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thanks

Answer 2

put $1$ in all places in adjacency marix according to direction given in edges for ex $p1$ to $p5$ there is path going so put $1$ in $p1$ row and $p5$ col but don't put $1$ in $p5$ to $p1$ because there is no path

Answer 3

to be clear that arrow is from p3 to p1

Answer 4

This is also a possibility based on the convention given in “Introduction to Graph Theory” by Douglas West.