for the analysis of structures, the first step consists of configuration processing followed by data generation. this step is the most time consuming part of the analysis for large-scale structures. in this paper new graph products called triangular and circular graph products are developed for the formation of the space structures. the graph products are extensively used in graph theory and co...

in this paper, the weighted szeged indices of cartesian product and corona product of twoconnected graphs are obtained. using the results obtained here, the weighted szeged indices ofthe hypercube of dimension n, hamming graph, c4 nanotubes, nanotorus, grid, t− fold bristled,sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

the wiener index $w(g)$ of a connected graph $g$‎ ‎is defined as $w(g)=sum_{u,vin v(g)}d_g(u,v)$‎ ‎where $d_g(u,v)$ is the distance between the vertices $u$ and $v$ of‎ ‎$g$‎. ‎for $ssubseteq v(g)$‎, ‎the {it steiner distance/} $d(s)$ of‎ ‎the vertices of $s$ is the minimum size of a connected subgraph of‎ ‎$g$ whose vertex set is $s$‎. ‎the {it $k$-th steiner wiener index/}‎ ‎$sw_k(g)$ of $g$ ...

A {\it graph product} $G$ on a $\Gamma$ is group defined as follows: For each vertex $v$ of there corresponding non-trivial $G_v$. The the quotient free product $G_v$ by commutation relations $[G_v,G_w]=1$ for all adjacent and $w$ in $\Gamma$. finitely presented has semistable fundamental at $\infty$} if some (equivalently any) finite connected CW-complex $X$ with $\pi_1(X)=G$, universal cover ...

In this work we prove that, given a simplicial graph Γ $\Gamma$ and family G $\mathcal {G}$ of linear groups over domain R $R$ , the product $\Gamma \mathcal is [ t ̲ ] $R[\underline{t}]$ where $\underline{t}$ tuple finitely many linearly independent variables. As consequence, obtain that any complex numbers again group numbers. This solves an open problem Hsu Wise (Michigan Math. J. 46 (1999), ...