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...

Predicating macroscopic influences of drugs on human body, like efficacy and toxicity, is a central problem of smallmolecule based drug discovery. Molecules can be represented as an undirected graph, and we can utilize graph convolution networks to predication molecular properties. However, graph convolutional networks and other graph neural networks all focus on learning node-level representat...

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) +  ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ∑νεV (H) f(v) + ∑νεE (H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥...

We present a graphical representation of the supersymmetry and the graphical calculation. Calculation is demonstrated for 4D Wess-Zumino model and for Super QED. The chiral operators are graphically expressed in an illuminating way. The tedious part of SUSY calculation, due to manipulating chiral suffixes, reduces considerably. The application is diverse. PACS. 02.10.Ox Copmbinatorics, graph th...

A graph G of order p and size q is called (a, d)-edge-antimagic total if there exists a bijection f : V(G) ∪ E(G) → {1, 2, . . . , p + q} such that the edge-weights, w(uv) = f(u) + f (v) + f (uv), uv ∈ E(G), form an arithmetic sequence with the first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study supe...

Here, we give a full proof of Theorem 1. Recall that an equivalent construction of the PAGA graphs is obtained by collapsing the graph G 1 to G t m leading to t super nodes. Accordingly, based on G t m, we can directly generate G m by (temporarily) adding m more nodes, each linking with a single edge, and then collapsing these m nodes to the (t+ 1)th super node. Let dt,i(v) denote the degree of...