جستجوی مقالات مرتبط با کلیدواژه "graph invariants" در نشریات گروه "ریاضی"

We introduce a fast method of computing the topological charge indices of simple graphs (molecules) which does not require matrices of large sizes. For the case of trees, we give a compact formula and in the general case we obtain upper and lower bounds for the charge indices. We give concrete examples of trees and molecules with their charge indices computed using our method.

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity coindex of some graph products such as lexicographic product, generalized hierarchical product, and strong product. Results are applied to compute the values of this eccentricity-based invariant for some chemical graphs and nanostructures such as hexagonal chain, linear phenylene chain, and zig-zag polyhex nanotube.

‎Let $G=(V,E)$ be a simple graph with $nge 3$ vertices‎, ‎$m$ edges‎ ‎and vertex degree sequence $Delta=d_1 ge d_2 ge cdots ge‎ ‎d_n=delta>0$‎. ‎Denote by $S={1, 2,ldots,n}$ an index set and by‎ ‎$J={I=(r_1, r_2,ldots,r_k) ‎, ‎| ‎, ‎1le r_1<r_2<cdots<r_kle‎ ‎n}$ a set of all subsets of $S$ of cardinality $k$‎, ‎$1le kle‎ ‎n-1$‎. ‎In addition‎, ‎denote by‎ $d_{I}=d_{r_1}+d_{r_2}+cdots+d_{r_k}$‎, ‎$1le kle n-1$‎, ‎$1le‎ ‎r_1<r_2<cdots<r_kle n-1$‎, ‎the sum of $k$ arbitrary vertex‎ ‎degrees‎, ‎where $Delta_{I}=d_{1}+d_{2}+cdots+d_{k}$ and‎ ‎$delta_{I}=d_{n-k+1}+d_{n-k+2}+cdots+d_{n}$‎. ‎We consider the following graph invariant‎ ‎$S_{alpha,k}(G)=sum_{Iin J}d_I^{alpha}$‎, ‎where $alpha$ is an‎ ‎arbitrary real number‎, ‎and establish its bounds‎. ‎A number of known bounds for various topological indices are obtained as special cases‎.