For a (molecular) graph, the hyper Zagreb index is defined as HM(G) = ∑ uv∈E(G) (dG(u) + dG(v)) 2 and the hyper Zagreb coindex is defined asHM(G) = ∑ uv/ ∈E(G) (dG(u)+dG(v)) 2. In this paper, the hyper Zagreb indices and its coindices of edge corona product graph, double graph and Mycielskian graph are obtained.

It is already known that for very small edge cuts in graphs, the crossing number of the graph is at least the sum of the crossing number of (slightly augmented) components resulting from the cut. Under stronger connectivity condition in each cut component that was formalized as a graph operation called zip product, a similar result was obtained for edge cuts of any size, and a natural question ...

The corona G◦H of two graphs G and H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining each i-th vertex of G to every vertex in the i-th copy of H. The neighborhood coronaG⋆H of two graphs G and H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the neighbors of the i-th vertex of G to every vertex in the i-th copy of H. In this p...

The reformulated Zagreb indices of a graph are obtained from the classical Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of the end vertices of the edge minus 2. In this paper, we study the behavior of the reformulated first Zagreb index and apply our results to different chemically interesting molecular graphs and nano-...

The metric dimension is quite a well-studied graph parameter. Recently, the adjacency metric dimension and the local metric dimension have been introduced. We combine these variants and introduce the local adjacency metric dimension. We show that the (local) metric dimension of the corona product of a graph of order n and some non-trivial graph H equals n times the (local) adjacency metric dime...

Logistics planning in disaster response phase involves dispatching commodities such as medical materials, personnel, food, etc. to affected areas as soon as possible to accelerate the relief operations. Since transportation vehicles in disaster situations can be considered as scarce resources, thus, the efficient usage of them is substantially important. In this study, we provide a dynamic vehi...