let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, the degree of $v$,denoted by $d(v)$, is defined as the minimum value if its out-degree and its in-degree.now let $d$ be a digraph with minimum degree $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...

a subset $s$ of vertices in a graph $g$ is called a geodetic set if every vertex not in $s$ lies on a shortest path between two vertices from $s$‎. ‎a subset $d$ of vertices in $g$ is called dominating set if every vertex not in $d$ has at least one neighbor in $d$‎. ‎a geodetic dominating set $s$ is both a geodetic and a dominating set‎. ‎the geodetic (domination‎, ‎geodetic domination) number...

generally, developing countries are not able to invest enough on r&d; therefore, they try to get benefit from knowledge spillover, as an external r&d.; this paper tries to investigate the impact of r&d; expenditures and imported intermediate goods, as a proxy for technology imports, on value added of iranian industries. to that end, we use a panel data set of iranian two-digit isic manufacturin...

Let $D$ be a finite and simple digraph with vertex set $V(D)$‎.‎A signed total Roman $k$-dominating function (STR$k$DF) on‎‎$D$ is a function $f:V(D)rightarrow{-1‎, ‎1‎, ‎2}$ satisfying the conditions‎‎that (i) $sum_{xin N^{-}(v)}f(x)ge k$ for each‎‎$vin V(D)$‎, ‎where $N^{-}(v)$ consists of all vertices of $D$ from‎‎which arcs go into $v$‎, ‎and (ii) every vertex $u$ for which‎‎$f(u)=-1$ has a...

Most existing distances between intuitionistic fuzzy sets are defined in linear plane representations in 2D or 3D space. Here, we define a new interpretation of intuitionistic fuzzy sets as a restricted spherical surface in 3D space. A new spherical distance for intuitionistic fuzzy sets is introduced. We prove that the spherical distance is different from those existing distances in that it is...

Let (G) be the domination number of graph G, thus a graph G is k -edge-critical if (G) 1⁄4 k ; and for every nonadjacent pair of vertices u and v, (Gþ uv) 1⁄4 k 1. In Chapter 16 of the book ‘‘Domination in Graphs— Advanced Topics,’’ D. Sumner cites a conjecture of E. Wojcicka under the form ‘‘3-connected 4-critical graphs are Hamiltonian and perhaps, in general (i.e., for any k 4), (k 1)-connec...

We study the local profiles of trees. We show that in contrast with the situation for general graphs, the limit set of k-profiles of trees is convex. We initiate a study of the defining inequalities of this convex set. Many challenging problems remain open. C © 2015 Wiley Periodicals, Inc. J. Graph Theory 00: 1–11, 2015

We find the maximum number of maximal independent sets in two families of graphs. The first family consists of all graphs with n vertices Contract grant sponsor: Award from DIMACS (partially; to V.R.V.); Contract grant sponsor: NSF VIGRE grant to the Rutgers University Department of Mathematics (partially; to V.R.V.). Journal of Graph Theory © 2006 Wiley Periodicals, Inc. 270 MAXIMAL INDEPENDEN...

A cycle C of a graph G is dominating if each component of GnC is edgeless. In the paper, we will give two sufficient conditions for each longest cycle of a 3-connected graph to be a dominating cycle. 2005 Wiley Periodicals, Inc. J Graph Theory 49: 135–150, 2005

Given a T-indistinguishability operator E defined between some fuzzy subsets of a universe of discourse X, this paper studies three ways to generate an indistinguishability operator on X compatible with E inspired by the tools used in approximate reasoning and on the duality principle. Of special interest are the cases when the fuzzy subsets determine a partition and a hard-partition of the uni...