The harmonic index is one of the most important indices in chemical and mathematical fields. It’s a variant of the Randić index which is the most successful molecular descriptor in structure-property and structureactivity relationships studies. The harmonic index gives somewhat better correlations with physical and chemical properties comparing with the well known Randić index. The harmonic ind...

Identifying graphs with extremal properties is an extensively studied topic in spectral graph theory. In this paper, we study the log-concavity of a type iteration sequence related to α -normal weighted incidence matrices which presented by Lu and Man for computing radius hypergraphs. By using results obtained about method some edge operations, will characterize completely k -graphs smallest am...

Let G be a connected graph; the edge Mostar index Moe(G) of is defined as Moe(G)=∑e=uv∈E(G)|mu(e)−mv(e)|, where mu(e) and mv(e) denote number edges in that are closer to vertex u than v u, respectively. In this paper, we determine upper bound for all bicyclic graphs identify extremal achieve bound.

Du, Zhou and Trinajstić [J. Math. Chem., 48, pp. 697–703, 2010] proved that in the set of n-vertex connected unicyclic graphs G with n ≥ 3, for –1 ≤ α < 0, the graph consisting of a triangle and n – 3 pendant vertices adjacent to the same vertex of this triangle is the unique graph with the minimum general sum-connectivity index. In this paper, using a graph transformation and several inequalit...

In 1869, Jordan proved that the set T of all finite groups can be represented as automorphism group a tree is containing trivial group, it closed under taken direct product lower orders in , and wreath member symmetric on n symbols again an element . The aim this paper to continue work another works by Klavik Zeman 2017 present class S for which each bicyclic graph minimal with property.

Let the trunk of a graph G be the graph obtained by removing all leaves of G. We prove that, for every integer c ≥ 2, there are at most finitely many trunks of semiharmonic graphs with cyclomatic number c — in contrast to the fact established by the last two of the present authors in their paper Semiharmonic Bicyclic Graphs (this journal) that there are infinitely many connected semiharmonic gr...

A simple graph is said to be reflexive if its second largest eigenvalue does not exceed 2. The property λ2 ≤ 2 is a hereditary one, i.e. any induced subgraph of a reflexive graph preserves this property and that is why reflexive graphs are usually represented by maximal graphs within a given class. Bicyclic graphs whose two cycles have a common path are called θ-graphs. We consider classes of m...

For a graph G = (V,E), the modified Schultz index of G is defined as S∗(G) = ∑ {u,v}⊆V (G) (dG(u) · dG(v))dG(u, v) where dG(u) (or d(u)) is the degree of the vertex u of G, and dG(u, v) is the distance between u and v. Let B(n) be the set of bicyclic graph with n vertices. In this paper, we study the modified Schultz index of B(n), graphs in B(n) with the smallest modified Schultz index S∗(G) a...

Bicyclic aziridines show exclusive photochromic behavior. Here, we summarize the results of optical and electrochemical properties, such as photochemical, solvatochromic, electrochromic andkinetic behavior of bicyclic aziridines linked to chalcone moieties. The photochromic process for conversion of closed photoisomers to open photoisomers for compounds 1-10 followed zero-order kinetics. For co...

Complex networks are ubiquitous in biological, physical and social sciences. Network robustness research aims at finding a measure to quantify network robustness. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks. Wiener type indices are known to depend both on the network's number of nodes and topology. The Wiener polarity index i...