Abstract
One of the tools, to research and investigation the structural dependence of various properties and some activities of chemical structures and networks is the topological indices of graphs. In this research work, we introduce novel indices of graphs which they based on the uphill degree of the vertices termed as uphill Zagreb topological indices. Exact formulae of these new indices for some important and famous families of graphs are established.
Highlights
In this research, by graphs, we mean undirected finite simple graph
We denote G = (V, E) for a graph, where V is the set of vertices and E is the set of edges
In this paper motivated by the large applications of topological indices and the concept of uphill domination, we introduce novel indices of graphs based on a new degree of the vertices termed as uphill Zagreb topological indices
Summary
By graphs, we mean undirected finite simple graph. We denote G = (V, E) for a graph, where V is the set of vertices and E is the set of edges. The uphill degree of the vertex v , denoted by dup(v ), is the number of vertices which v uphill adjacent them, that means dup(v ) = |Nup(v )|. Suppose G be a graph, for any two vertices u and v , where u is uphill adjacent to v , if d (u) < d(v ).
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