On the dot product of graphs over monogenic semigroups

Introducing New Exponential Zagreb Indices for Graphs

“…As mentioned in [30], some chemically interesting graphs can be obtained by different graph operations which are applied onto some general or particular graphs, so it is essential to study such graph operations to understand how they are related to the corresponding topological indices of the original graphs. So far, first and second Zagreb indices have been largely studied under some graph operations (see, for instance, [3,8,11,[30][31][32][33][34][35]).…”

On the Wiener Index of the Dot Product Graph over Monogenic Semigroups

“…This equality holds if n − k + a > n or a = 0 S n and n − t + b > n or a = 0 S n . Alternatively, all elements of S can be thought to form a matrix [C] (n+1)×(n+1) for n ∈ N, in [12]:…”

“…The following result will be used in the rest of the paper: 12]). (S) is always connected and its diameter is equal to 2, that is diam( (S)) = 2.…”

“…Akgüneş has defined the graph of monogenic semigroups in [11] in a similar manner. The dot product graphs of monogenic semigroups have been studied in [12].…”

An Application of Sombor Index over a Special Class of Semigroup Graph

“…By utilizing the idea defined in [5,6], the authors obtained a new graph related to monogenic semigroups in [7]. e vertices of this graph are all nonzero elements in S M and for any two different vertices x i and x j where (1 ≤ i, j ≤ n) are linked to each other, if and only if i + j > n. ere are many studies concerning monogenic semigroup graphs which were published by Akgünes ¸et al (see for example [8][9][10]).…”