Abstract
Edge deletion and addition to a graph is an important combinatorial method in Graph Theory which enables one to calculate some properties of a graph by means of similar graphs. The effect of edge addition on the first and second Zagreb indices was recently investigated by the authors. In this sequel paper, we consider the change in the first and second Zagreb indices of any simple graph G when an arbitrary edge is deleted. Further, we calculate the change in the first Zagreb index when an arbitrary number of edges are deleted. This method can be used to calculate the first and second Zagreb indices of larger graphs in terms of the Zagreb indices of smaller graphs. As some examples, we give some inequalities for the change of Zagreb indices for path, cycle, star, complete, complete bipartite, and tadpole graphs.
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