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.

Recall that a (hyper)graph is d-degenerate if every of its nonempty subgraphs has a vertex of degree at most d. Every d-degenerate (hyper)graph is (easily) (d + 1)colorable. A (hyper)graph is almost d-degenerate if it is not d-degenerate, but every its proper subgraph is d-degenerate. In particular, if G is almost (k − 1)-degenerate, then after deleting any edge it is k-colorable. For k ≥ 2, we...

The matching preclusion number of a graph G, mp(G), is the minimum number of edges whose deletion leaves a resulting graph that has neither perfect matchings nor almost perfect matchings. Besides its theoretical linkage with conditional connectivity and extremal graph theory, the matching preclusion number is a measure of robustness in interconnection networks. In this paper we develop general ...

Given a family of (hyper)graphs F a (hyper)graph G is said to be F-saturated if G is F -free for any F ∈ F but for any edge e in the complement of G the (hyper)graph G + e contains some F ∈ F . We survey the problem of determining the minimum size of an F-saturated (hyper)graph and collect many open problems and conjectures.

university course timetabling is a complex optimizationproblem. there are many components like departments, faculties, rooms,and students making the problem huge and difficult to solve. eachcomponent enforces a set of normally conflicting constraints on thesolution space. the problem will be solved if courses are scheduled indifferent rooms and within some specific time slots such that a set of...

Let $R$ be a commutative ring with identity and $mathbb{A}(R)$ be the set   of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $mathbb{A}_P(R)=mathbb{A}(R)cap mathbb{P}(R)setminus {(0)}$, where   $mathbb{P}(R)$ is...

We have discovered a star, SDSS J090745.0+024507, leaving the Galaxy with a heliocentric radial velocity of +853± 12 km s, the largest velocity ever observed in the Milky Way halo. The star is either a hot blue horizontal branch star or a B9 main sequence star with a heliocentric distance ∼55 kpc. Corrected for the solar reflex motion and to the local standard of rest, the Galactic rest-frame v...

A graph G is said to be hyper-connected if the removal of every minimum cut creates exactly two connected components, one of which is an isolated vertex. In this paper, we first generalize the concept of hyper-connected graphs to that of semi-hyper-connected graphs: a graph G is called semi-hyper-connected if the removal of every minimum cut of G creates exactly two components. Then we characte...

In graph theory, as in many fields of mathematics, one is often interested in finding the maxima or minima of certain functions and identifying the points of optimality. We consider a variety of functions on graphs and hypegraphs and determine the structures that optimize them. A central problem in extremal (hyper)graph theory is that of finding the maximum number of edges in a (hyper)graph tha...