The area of graph theory (GT) is rapidly expanding and playing a significant role in cheminformatics, mostly mathematics chemistry to develop different physicochemical, chemical structure, their properties. manipulation study graphical details are made feasible by using numerical structure invariant. Investigating these characteristics topological indices (TIs) possible the discipline mathemati...

The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path Pn of length n, the crossing numbers of Cartesian products G Pn for all connected graphs G on five vertices are also known. In this paper, the crossing numbers of Cartesian products G Pn for graphs G of order six are studied. Let H denote the unique tree of order si...

24 A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection 25 l : V → {1, . . . , n} such that the weight of every vertex v, computed as the sum 26 of the labels on the vertices in the open neighborhood of v, is a constant. 27 In this paper, we show that hypercubes with dimension divisible by four 28 are not distance magic. We also provide some positive results by providing ...

Let G = (V,E) be a graph. For a non-empty subset of vertices S ⊆ V , and vertex v ∈ V , let δS(v) = |{u ∈ S : uv ∈ E}| denote the cardinality of the set of neighbors of v in S, and let S = V − S. Consider the following condition: δS(v) ≥ δS(v) + k, (1) which states that a vertex v has at least k more neighbors in S than it has in S. A set S ⊆ V that satisfies Condition (1) for every vertex v ∈ ...

Sandi Klavžar and Zehui Shao Faculty of Mathematics and Physics, University of Ljubljana, Slovenia Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, China School of Info...