Sufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs L. Volkmann RWTH Aachen University author text article 2016 eng Let D be a digraph with vertex set V(D) .For vertex v 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  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randic index, the order and the minimum degree when  Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 1 v. 1 no. 2016 1 13 http://comb-opt.azaruniv.ac.ir/article_13514_2c29013911bbc87b1dc4be81c6823349.pdf dx.doi.org/10.22049/cco.2016.13514 The minus k-domination numbers in graphs N. Dehgardi Sirjan University of Technology, Sirjan 78137, Iran author text article 2016 eng For any integer  ‎, ‎a minus  k-dominating function is a‎function  f‎ : ‎V (G)  {-1,0‎, ‎1} satisfying w) for every  vertex v, ‎where N(v) ={u V(G) | uv  E(G)}  and N[v] =N(v)\cup {v}. ‎The minimum of ‎the values of  v)‎, ‎taken over all minus‎k-dominating functions f,‎ is called the minus k-domination‎number and is denoted by $\gamma_k^-(G)$ ‎. ‎In this paper‎, ‎we ‎introduce the study of minus  k-domination in graphs and we present‎ ‎several sharp lower bounds on the minus  k-domination number for general graphs‎. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 1 v. 1 no. 2016 15 28 http://comb-opt.azaruniv.ac.ir/article_13534_842d7e5cc29617870d3b17a192a370e4.pdf dx.doi.org/10.22049/cco.2016.13534 New bounds on proximity and remoteness in graphs P. Dankelmann University of Johannesburg author text article 2016 eng The average distance of a vertex $v$ of a connected graph $G$is the arithmetic mean of the distances from $v$ to allother vertices of $G$. The proximity $pi(G)$ and the remoteness $rho(G)$of $G$ are defined as the minimum and maximum averagedistance of the vertices of $G$. In this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter and radius. Among other results we show that in a graph of order$n$ and minimum degree $delta$ the difference betweendiameter and proximity and the difference betweenradius and proximity cannot exceed $frac{9n}{4(delta+1)}+c_1$ and $frac{3n}{4(delta+1)}+c_2$, respectively, for constants $c_1$ and $c_2$ which depend on $delta$but not on $n$. These bounds improve bounds byAouchiche and Hansen cite{AouHan2011} in terms oforder alone by about a factor of $frac{3}{delta+1}$. We further give lower bounds on the remoteness interms of diameter or radius. Finally we show thatthe average distance of a graph, i.e., the average ofthe distances between all pairs of vertices, cannotexceed twice the proximity. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 1 v. 1 no. 2016 29 41 http://comb-opt.azaruniv.ac.ir/article_13543_99e338e777d53b2fb451bb25a4de0578.pdf dx.doi.org/10.22049/cco.2016.13543 The convex domination subdivision number of a graph M. Dettlaff Gdańsk University of Technology author S. Kosari Azarbaijan Shahid Madani University author M. Lemańska Gdańsk University of Technology author S.M. Sheikholeslami Azarbaijan Shahid Madani University author text article 2016 eng Let $G=(V,E)$ be a simple graph. A set $Dsubseteq V$ is adominating set of $G$ if every vertex in $Vsetminus D$ has atleast one neighbor in $D$. The distance $d_G(u,v)$ between twovertices $u$ and $v$ is the length of a shortest $(u,v)$-path in$G$. An $(u,v)$-path of length $d_G(u,v)$ is called an$(u,v)$-geodesic. A set $Xsubseteq V$ is convex in $G$ ifvertices from all $(a, b)$-geodesics belong to $X$ for any twovertices $a,bin X$. A set $X$ is a convex dominating set if it isconvex and dominating set. The {em convex domination number}$gamma_{rm con}(G)$ of a graph $G$ equals the minimumcardinality of a convex dominating set in $G$. {em The convexdomination subdivision number} sd$_{gamma_{rm con}}(G)$ is theminimum number of edges that must be subdivided (each edge in $G$can be subdivided at most once) in order to increase the convexdomination number. In this paper we initiate the study of convexdomination subdivision number and we establish upper bounds forit. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 1 v. 1 no. 2016 43 56 http://comb-opt.azaruniv.ac.ir/article_13544_b044108d0b0eedf90a89cf1f47c4f8e0.pdf dx.doi.org/10.22049/cco.2016.13544 More skew-equienergetic digraphs Ch. Adiga University of Mysore author Rakshith B R University of Mysore author text article 2016 eng Two digraphs of same order are said to be skew-equienergetic if their skew energies are equal. One of the open problems proposed by Li and Lian was to construct non-cospectral skew-equienergetic digraphs on n vertices. Recently this problem was solved by Ramane et al. In this  paper, we give some new methods to construct new skew-equienergetic digraphs. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 1 v. 1 no. 2016 57 73 http://comb-opt.azaruniv.ac.ir/article_13545_0f42ad1856ecb7c77844ab63bd68ed35.pdf dx.doi.org/10.22049/cco.2016.13545 Bounds on the restrained Roman domination number of a graph H. Abdollahzadeh Ahangar Babol Noshirvani University of Technology author S.R. Mirmehdipour Babol Noshirvani University of Technology author text article 2016 eng A {em Roman dominating function} on a graph $G$ is a function$f:V(G)rightarrow {0,1,2}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex$v$ for which $f(v) =2$. {color{blue}A {em restrained Roman dominating}function} $f$ is a {color{blue} Roman dominating function if the vertices with label 0 inducea subgraph with no isolated vertex.} The weight of a restrained Roman dominating function isthe value $omega(f)=sum_{uin V(G)} f(u)$. The minimum weight of arestrained Roman dominating function of $G$ is called the { emrestrained Roman domination number} of $G$ and denoted by $gamma_{rR}(G)$.In this paper we establish some sharp bounds for this parameter. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 1 v. 1 no. 2016 75 82 http://comb-opt.azaruniv.ac.ir/article_13556_af7da9ddc41c8343edb4835aaab47c2c.pdf dx.doi.org/10.22049/cco.2016.13556