HF-Index and Y-Index of Some New Graph of Operations

In this paper we derive HF index of some graph operations containing join, Cartesian Product, Corona Product of graphs and compute the Y index of new operations of graphs related to the join of graphs.

On Independent Secondary Dominating Sets in Generalized Graph Products

In 2008, Hedetniemi et al. introduced (1,k)-domination in graphs. The research on this concept was extended to the problem of existence of independent (1,k)-dominating sets, which is an NP-complete problem. In this paper, we consider independent (1,1)- and (1,2)-dominating sets, which we name as (1,1)-kernels and (1,2)-kernels, respectively. We obtain a complete characterization of generalized corona of graphs and G-join of graphs, which have such kernels. Moreover, we determine some graph parameters related to these sets, such as the number and the cardinality. In general, graph products considered in this paper have an asymmetric structure, contrary to other many well-known graph products (Cartesian, tensor, strong).

Star coloring under some graph operations

A star coloring of a graph [Formula: see text] is a proper coloring of [Formula: see text] such that no path of length 3 in [Formula: see text] is bicolored. In this paper, the star chromatic number of join of graphs is computed. Some sharp bounds for the star chromatic number of corona, lexicographic, deleted lexicographic and hierarchical product of graphs together with a conjecture on the star chromatic number of lexicographic product of graphs are also presented.

Irregularity Measures of Subdivision Vertex-Edge Join of Graphs

The study of graphs and networks accomplished by topological measures plays an applicable task to obtain their hidden topologies. This procedure has been greatly used in cheminformatics, bioinformatics, and biomedicine, where estimations based on graph invariants have been made available for effectively communicating with the different challenging tasks. Irregularity measures are mostly used for the characterization of the nonregular graphs. In several applications and problems in various areas of research like material engineering and chemistry, it is helpful to be well-informed about the irregularity of the underline structure. Furthermore, the irregularity indices of graphs are not only suitable for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies but also for a number of chemical and physical properties, including toxicity, enthalpy of vaporization, resistance, boiling and melting points, and entropy. In this article, we compute the irregularity measures including the variance of vertex degrees, the total irregularity index, the σ irregularity index, and the Gini index of a new graph operation.

Szeged-type indices of subdivision vertex-edge join (SVE-join)

In this article, we compute the vertex Padmakar-Ivan (PIv ) index, vertex Szeged (Szv ) index, edge Padmakar-Ivan (PIe ) index, edge Szeged (Sze ) index, weighted vertex Padmakar-Ivan (wPIv ) index, and weighted vertex Szeged (wSzv ) index of a graph product called subdivision vertex-edge join of graphs.