Journal of Prime Research in Mathematics

# Zagreb indices and coindices of product graphs

K. Pattabiraman
Department of Mathematics, Faculty of Engineering and Technology, Annamalai University, Annamalainagar 608 002, India.
S. Nagarajan
Department of Mathematics, Kongu Arts and Science College, Erode – 638 107, India.
M. Chendrasekharan
Department of Mathematics, Erode Arts and Science College, Erode – 638 009, India.

$$^{1}$$Corresponding Author: pramank@gmail.com

### Abstract

For a (molecular) graph, the first Zagreb index $$M_1$$ is equal to the sum of squares of the degrees of vertices, and the second Zagreb index $$M_2$$ is equal to the sum of the products of the degrees of pairs of adjacent vertices. Similarly, the first and second Zagreb coindices are defined as $$\overline{M}_1(G) = \sum_{ uv \notin E(G)} (d_G(u) + d_G(v))$$ and $$\overline{M}_2(G)=\sum_{ uv \notin E(G)} d_G(u)d_G(v)$$. In this paper, we compute the Zagreb indices and coindices of strong, tensor and edge corona product of two connected graphs. We apply some of our results to compute the Zagreb indices and coindices of open and closed fence graphs.

#### Keywords:

Zagreb index, Zagreb coindex, strong product, tensor product, edge corona product.