Abstract We initiate a study of the Euclidean distance degree in context sparse polynomials. Specifically, we consider hypersurface $$f=0$$ f = 0 defined by polynomial f that is general given its support, such support contains origin. show equals mixed ...

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

Let G be a finite connected graph. The degree distance D′(G) of G is defined as ∑ {u,v}⊆V (G)(deg u + deg v) dG(u, v), where degw is the degree of vertex w and dG(u, v) denotes the distance between u and v in G. In this paper, we give asymptotically sharp upper bounds on the degree distance in terms of order and edge-connectivity.

Let G be a connected graph with n vertices. Then the class of graphs having vertices is denoted by Gn. The subclass 5 cycles are Gn5. classification G∈Gn5 depends on number edges and sum degrees graph. Any in Gn5 contains five linearly independent at least n+3 5-cyclic must equal to twice n+4. In this paper, minimum degree distance cyclic investigated. To find some transformations T have been d...