The book titled "Vertex coloring for the analysis of Gaussian & Laplacian Image Pyramid" was written for the purpose of bridging the field of Graph Theory with Digital Image Processing. The book belongs the innovation of applying vertex coloring as a color code for image compression purpose. Nowadays a lot of research is being performed in the field of Image Compression and Vertex coloring. But the current book comprises an algorithm for the image compression purpose by using the Vertex coloring. The authors hope that the current work will help the researchers and scientists for the further development in the field of Image Compression by Vertex Coloring.