We propose a novel graph matching algorithm that uses ideas from graph signal processing to match vertices of graphs using alternative graph representations. Specilically, we consider a multi-scale heat diffusion on the graphs to create multiple weighted graph representations that incorporate both direct adjacencies as well as local structures induced from the heat diffusion. Then a multi-objective optimization method is used to match vertices across all pairs of graph representations simultaneously. We show that our proposed algorithm performs significantly better than the algorithm that only uses the adjacency matrices, especially when the number of known latent alignments between vertices (seeds) is small. We test the algorithm on a set of graphs and show that at the low seed level, the proposed algorithm performs at least 15-35% better than the traditional graph matching algorithm.