On the rank of weighted graphs

Abstract

Let G w be a weighted graph and A(G w ) be the adjacency matrix of G w . The rank of G w is the rank of A(G w ). If the weight of each edge of G w is 1 or −1, G w is also called a signed graph. In this paper, we characterize weighted graphs with rank 2, weighted K 4 -free graphs with rank 3 and weighted graphs containing pendent vertices with rank 4. We also characterize signed graphs with rank 4. ARTICLE HISTORY