Question

If a connected Graph (G) contains n vertices what would be the rank of its incidence matrix?

(a) n-1

(b) values greater than n are possible

(c) values less than n-1 are possible

(d) insufficient Information is given

My question is taken from Incidence Matrix and Graph Structured Stack topic in section Graph of Data Structures & Algorithms I

This question was posed to me by my college professor while I was bunking the class.

Answer 1

The correct option is (a) n-1

The best I can explain: Every column of the incidence matrix may contain only +1 and -1 as non zero entries rank would be less than n.