LAUSR

Let R be a commutative semiring with nonzero identity and H be a multiplicative-prime subset of R. The generalized total graph of a commutative semiring R is the (undirected) graph $$GT_{H}(R)$$GTH(R) whose vertices are all elements of R and two distinct vertices x and y are adjacent if and only if $$x+y\in H$$x+y∈H. In this paper, we investigate the structure of $$GT_{H}(R)$$GTH(R) and we also study the two (induced) subgraphs $$GT_{H}(H)$$GTH(H) and $$GT_{H}(R{\setminus } H)$$GTH(R\H) with vertex-sets H and $$R{\setminus } H$$R\H.