New graph invariants, named exponential Zagreb indices, are introduced for more than one type of Zagreb index. After that, in terms of exponential Zagreb indices, lists on equality results over special graphs are presented as well as some new bounds on unicyclic, acyclic, and general graphs are obtained. Moreover, these new graph invariants are determined for some graph operations.

Algebraic study of graphs is a relatively recent subject which arose in two main streams: One is named as the spectral graph theory and the second one deals with graphs over several algebraic structures. Topological graph indices are widely-used tools in especially molecular graph theory and mathematical chemistry due to their time and money saving applications. The Wiener index is one of these indices which is equal to the sum of distances between all pairs of vertices in a connected graph. The graph over the nite dot product of monogenic semigroups has recently been dened and in this paper, some results on the Wiener index of the dot product graph over monogenic semigroups are given.

Topolojik indekslerin matematiksel kimyada kulanım alanı bulunmaktadır. Uzaklık-bazlı topolojik indekslerin ise moleküler graf teoride oldukça önemi vardır. Harary indeksi uzaklık-bazlı bir graf değişmezidir. Yakın zamanda cebirsel bir yapı üzerinde nokta çarpım grafı çalışıldı. Bu çalışmada da bu grafın Harary indeksi verilecektir.