We give a linear-time algorithm to compute the cutwidth of threshold graphs, thereby resolving the computational complexity of cutwidth on this graph class. Threshold graphs are a well-studied subclass of interval graphs and of split graphs, both of which are unrelated subclasses of chordal graphs. To complement our result, we show that cutwidth is NPcomplete on split graphs, and consequently a...

A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.

Say a set H of graphs is heroic if there exists k such that every graph containing no member of H as an induced subgraph has cochromatic number at most k. (The cochromatic number of G is the minimum number of stable sets and cliques with union V (G).) Assuming an old conjecture of Gyárfás and Sumner, we give a complete characterization of the finite heroic sets. This is a consequence of the fol...

A parallel knock-out scheme for a graph proceeds in rounds in each of which each surviving vertex eliminates one of its surviving neighbours. A graph is KO-reducible if there exists such a scheme that eliminates every vertex in the graph. The Parallel Knock-Out problem is to decide whether a graph G is KO-reducible. This problem is known to be NP-complete and has been studied for several graph ...

in this paper, some applications of our earlier results in working with chemical graphs arepresented.

In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G ◦H of a connected graph G that is not complete by a graph H, we show that it is edge-transitive if and only if G is edge-transitive and H is edgeless. If the first factor of G ◦H is non-trivial and complete, then G ◦H is edge-transitive if and only if H is the lexicogr...

We give a linear-time algorithm to compute the cutwidth of threshold graphs, thereby resolving the computational complexity of cutwidth on this graph class. Although our algorithm is simple and intuitive, its correctness proof relies on a series of non-trivial structural results, and turns out to be surprisingly complex. Threshold graphs are a well-studied subclass of interval graphs and of spl...

the dispersibility of graphene is modeled as a mathematical function of the molecular structure of solvent represented by simplified molecular input-line entry systems (smiles) together with the graph of atomic orbitals (gao). the gao is molecular graph where atomic orbitals e.g. 1s1, 2p4, 3d7 etc., are vertexes of the graph instead of the chemical elements used as the graph vertexes in the tra...