The combined edges systems, which are the work’s central idea, used to introduce and investigate C-space in this paper. We crucial necessary stepping stone for concepts of c-derived graphs, c-closed c-closure.

We present exact solutions for the size of giant connected component (GCC) graphs composed higher-order homogeneous cycles, including weak cycles and cliques, following bond percolation. use our theoretical result to find location percolation threshold model, providing analytical where possible. expect results derived here be useful a wide variety applications graph theory, epidemiology, lattic...

cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. actually,the origin of this concept came back to richard brualdi's problems that are proposed in cite{braldi}:let $g_n$ and $g'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2 g...

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.

let $gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. denote by $upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. in the classes of graphs $gamma_{n,kappa}$ and $upsilon_{n,beta}$, the elements having maximum augmented zagreb index are determined.

The line graph L(G) of a graph G is defined to have as its vertices the edges of G, with two being adjacent if the corresponding edges share a vertex in G. Line graphs have a rich history. The name line graph was first used by Harary and Norman in 1960. But line graphs were the subject of investigation as far back as 1932 in a paper by H. Whitney in which he showed that for connected graphs, ed...

normal 0 false false false en-us x-none ar-sa background: robotic needle insertion in biological tissues has been known as one the most applicable procedures in sampling, robotic injection and different medical therapies and operations. objective: in this paper, we would like to investigate the effects of angular velocity in soft tissue insertion procedure by considering force-displacement diag...

in this paper, we determine the degree distance of the complement of arbitrary mycielskian graphs. it is well known that almost all graphs have diameter two. we determine this graphical invariant for the mycielskian of graphs with diameter two.

Graphs are often used as models to solve problems in computer science, mathematics, and biology. A pancake sorting problem is modeled using a graph whose classes include burnt graphs, signed permutation restricted graphs. The network cost degree × diameter. Finding with small like finding good algorithm. We propose novel recursively divided (RDP) that has smaller than other pancake-like In the ...