In this paper, we show that in the class of graphs of order n and given (vertex or edge) connectivity equal to k (or at most equal to k), 1 ? k ? n - 1, the graph Kk + (K1? Kn-k-1) is the unique graph such that zeroth-order general Randic index, general sum-connectivity index and general Randic connectivity index are maximum and general hyper-Wiener index is minimum provided ? > 1. Also, for 2-connected (or 2-edge connected) graphs and ? > 0 the unique graph minimizing these indices is the n-vertex cycle Cn.

A vertex irregular total -labeling of a -graph is a labeling such that the weights of the vertices are different for all vertices. The total vertex irregularity strength is the minimum for which ha...

In recent years, several structure-based properties of the molecular graphs are understood through the chemical graph theory. The molecular graph G of a molecule consists of vertices and edges, where vertices represent the atoms in a molecule and edges represent the chemical bonds between these atoms. A numerical quantity that gives information related to the topology of the molecular graphs is called a topological index. Several topological indices, contributing to chemical graph theory, have been defined and vastly studied. Recent inclusions in the class of the topological indices are the K-Banhatti indices. In this paper, we established the precise formulas for the first and second K-Banhatti, modified K-Banhatti, K-hyper Banhatti, and hyper Revan indices of silicon carbide Si2C3-III[n, m]. In addition, we present the graphical analysis along with the comparison of these indices for Si2C3-III[n, m].

Chemical graph theory comprehends the basic properties of an atomic graph. The sub-atomic diagrams are the graphs that are comprised of particles called vertices and the covalent bond between them are called edges. The eccentricity ${ϵ}_u$ of vertex u in an associated graph G, is the separation among u and a vertex farthermost from u. In this article, we consider the precious stone structure of cubic carbon and registered Eccentric-connectivity index $\xi \left(G\right)$ , Eccentric connectivity polynomial $ECP(G,x)$ and Connective Eccentric index $C^{\xi }\left(G\right)$ of gem structure of cubic carbon for n-levels.

This study focuses on finding super edge-magic total (SEMT) labeling and deficiency of imbalanced fork and disjoint union of imbalanced fork with star, bistar and path; in addition, the SEMT strength for Imbalanced Fork is investigated.

A graph ℘ is said to be edge-magic total (EMT if there is a bijection Υ : V(℘) ∪ E(℘) → {1, 2, …, |V(℘) ∪ E(℘)|} s.t., Υ(υ) + Υ(υν) + Υ(ν) is a constant for every edge υν ∈ E(℘). An EMT graph ℘ will be called strong edge-magic total (SEMT) if Υ(V(℘)) = {1, 2, …, |V(℘)|}. The SEMT strength, sm(℘), of a graph ℘ is the minimum of all magic constants a(Υ), where the minimum runs over all the SEMT valuations of ℘, this minimum is defined only if the graph has at least one such SEMT valuation. Furthermore, the SEMT deficiency of a graph ℘, μ_s(℘), is either the minimum non-negative integer n such that ℘ ∪ nK₁ is SEMT or +∞ if there will be no such integer n. In this paper, we will present the strong edge-magicness and deficiency of disjoint union of 2-sided generalized comb with bistar, path and caterpillar, moreover we will evaluate the SEMT strength for 2-sided generalized comb.