a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

A D-disc around a vertex v of a graph G = (V,E) is the subgraph induced by all vertices of distance at most D from v. We show that the structure of an outerplanar graph on n vertices is determined, up to modification (insertion or deletion) of at most n edges, by a set of D-discs around the vertices, for D = D( ) that is independent of the size of the graph. Such a result was already known for ...

We present an algorithm that supports operations for modifying a split graph by adding edges or vertices and deleting edges, such that after eachmodification the graph is repaired to become a split graph in a minimal way. In particular, if the graph is not split after the modification, the algorithm computes a minimal, or if desired even a minimum, split completion or deletion of themodified gr...

let $g$ be a group. the order graph of $g$ is the (undirected)graph $gamma(g)$,those whose vertices are non-trivial subgroups of $g$ and two distinctvertices $h$ and $k$ are adjacent if and only if either$o(h)|o(k)$ or $o(k)|o(h)$. in this paper, we investigate theinterplay between the group-theoretic properties of $g$ and thegraph-theoretic properties of $gamma(g)$. for a finite group$g$, we s...

the noncommuting graph $nabla (g)$ of a group $g$ is asimple graph whose vertex set is the set of noncentral elements of$g$ and the edges of which are the ones connecting twononcommuting elements. we determine here, up to isomorphism, thestructure of any finite nonabeilan group $g$ whose noncommutinggraph is a split graph, that is, a graph whose vertex set can bepartitioned into two sets such t...

let $n,t_1,...,t_k$ be distinct positive integers. a toeplitz graph $g=(v, e)$ denoted by $t_n$ is a graph, where $v ={1,...,n}$ and $e= {(i,j) : |i-j| in {t_1,...,t_k}}$.in this paper, we present some results on decomposition of toeplitz graphs.

in this paper we define the removable cycle that, if $im$ is a class of graphs, $gin im$, the cycle $c$ in $g$ is called removable if $g-e(c)in im$. the removable cycles in eulerian graphs have been studied. we characterize eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for eulerian graph to have removable cycles h...

The title compound, C(3)H(3)N(3)S(3), is a triclinic modification. The other reported modification crystallizes with just one mol-ecule in the asymmetric unit, [Guo et al. (2006 ▶). Cryst. Growth Des.6, 846-848] and was solved by power X-ray diffraction data. The present modification has Z' = 2. In the crystal, mol-ecules are linked by strong intra-molecular N-H⋯S hydrogen bonds with set graph-...

Based on the principles of equalized sliding coefficients and equalized teeth bending strength, the optimization mathematical model for calculating and allocating the addendum modification coefficients of involute cylindrical gear is firstly established. Then the measures to calculate the tooth parameters in real-time during the optimization steps are achieved. Finally, the optimization program...

Pairwise comparison matrices are often used in Multi-attribute Decision Making for weighting the attributes or for the evaluation of the alternatives with respect to a criteria. Matrices provided by the decision makers are rarely consistent and it is important to index the degree of inconsistency. In the paper, the minimal number of matrix elements by the modification of which the pairwise comp...