On the first Zagreb index of graphs with Self-Loops
Shashwath S. Shetty, Arathi Bhat K
Abstract
Some of the most comprehensively studied degree-based topological indices are the Zagreb indices. The first Zagreb index M1(G) of a graph G is defined as the sum of squares of the degrees of the vertices. Let X⊆V(G) and let GX be the graph obtained from the simple graph G, by attaching a self-loop to each of its vertices belonging to X. In this article, some sharp bounds for the first Zagreb index of graphs with self-loops using various parameters has been put forward.
Topics & Concepts
CombinatoricsMathematicsGraphSimple graphLoop (graph theory)Topological indexDiscrete mathematicsGraph theory and applicationsComputational Drug Discovery MethodsSynthesis and Properties of Aromatic Compounds