‎in this paper‎, ‎we define the common minimal dominating signed‎ ‎graph of a given signed graph and offer a structural‎ ‎characterization of common minimal dominating signed graphs‎. ‎in‎ ‎the sequel‎, ‎we also obtained switching equivalence‎ ‎characterizations‎: ‎$overline{s} sim cmd(s)$ and $cmd(s) sim‎ ‎n(s)$‎, ‎where $overline{s}$‎, ‎$cmd(s)$ and $n(s)$ are complementary‎ ‎signed gra...

let $p$ be a prime number and $n$ be a positive integer. the graph $g_p(n)$ is a graph with vertex set $[n]={1,2,ldots ,n}$, in which there is an arc from $u$ to $v$ if and only if $uneq v$ and $pnmid u+v$. in this paper it is shown that $g_p(n)$ is a perfect graph. in addition, an explicit formula for the chromatic number of such graph is given.

The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

the chromatic number of a graph g, denoted by χ(g), is the minimum number of colors such that g can be colored with these colors in such a way that no two adjacent vertices have the same color. a clique in a graph is a set of mutually adjacent vertices. the maximum size of a clique in a graph g is called the clique number of g. the turán graph tn(k) is a complete k-partite graph whose partition...

Depuis 1980, les politiques publiques suisses préconisent une utilisation rationnelle du sol afin d’éviter de consommer des espaces agricoles pour accueillir le développement urbain. Dans cette perspective, canton Genève a modifié en 2013 sa législation densifier zones résidentielles pavillonnaires. Cette pression urbaine s’est faite au détrim...

The book Synonymy and Semantic Classification by Karen Sparck Jones was published in 1986 as the first volume of Edinburgh Information Technology Series on computer science and artificial intelligence. The book is interesting both in its content and in some circumstances of its publication. The main part of the book comprises Sparck Jones's Ph.D. thesis, approved at the University of Cambridge ...

for a graph $g$ let $gamma (g)$ be its domination number. we define a graph g to be (i) a hypo-efficient domination graph (or a hypo-$mathcal{ed}$ graph) if $g$ has no efficient dominating set (eds) but every graph formed by removing a single vertex from $g$ has at least one eds, and (ii) a hypo-unique domination graph (a hypo-$mathcal{ud}$ graph) if $g$ has at least two minimum dominating sets...

Depuis le milieu des années 2000, chercheurs travaillent activement sur stockage du carbone par minéralisation avec une étape importante franchie en 2016 grâce aux résultats projet européen CarbFix mené Islande. Depuis, cette technologie a été déployée au niveau industriel la centrale géothermique d’Hellisheiði et combin&#23...

The purpose of this paper is the study of Cayley graph associated to a semihypergroup(or hypergroup). In this regards first  we associate a Cayley graph to every semihypergroup and then we study theproperties of this graph, such as  Hamiltonian cycles in this  graph.  Also, by some of examples we will illustrate  the properties and behavior of  these Cayley  graphs, in particulars we show that ...