Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
1
2016
06
30
Sufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs
1
13
EN
L.
Volkmann
RWTH Aachen University
volkm@math2.rwth-aachen.de
10.22049/cco.2016.13514
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.
Digraphs,Edge-connectivity,Maximally edge-connected digraphs,Zeroth-order general Randic index
http://comb-opt.azaruniv.ac.ir/article_13514.html
http://comb-opt.azaruniv.ac.ir/article_13514_2c29013911bbc87b1dc4be81c6823349.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
1
2016
06
01
The minus k-domination numbers in graphs
15
28
EN
N.
Dehgardi
Sirjan University of Technology, Sirjan 78137, Iran
ndehgardi@gmail.com
10.22049/cco.2016.13534
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.
Minus $k$-dominating function,minus $k$-domination number,graph
http://comb-opt.azaruniv.ac.ir/article_13534.html
http://comb-opt.azaruniv.ac.ir/article_13534_842d7e5cc29617870d3b17a192a370e4.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
1
2016
06
01
New bounds on proximity and remoteness in graphs
29
41
EN
P.
Dankelmann
University of Johannesburg
pdankelmann@uj.ac.za
10.22049/cco.2016.13543
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.
diameter,radius,proximity,remoteness,distance
http://comb-opt.azaruniv.ac.ir/article_13543.html
http://comb-opt.azaruniv.ac.ir/article_13543_99e338e777d53b2fb451bb25a4de0578.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
1
2016
08
08
The convex domination subdivision number of a graph
43
56
EN
M.
Dettlaff
Gdańsk University of Technology
mdettlaff@mif.pg.gda.pl
S.
Kosari
Azarbaijan Shahid Madani University
M.
Lemańska
Gdańsk University of Technology
magda@mif.pg.gda.pl
S.M.
Sheikholeslami
Azarbaijan Shahid Madani University
s.m.sheikholeslami@azaruniv.edu
10.22049/cco.2016.13544
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.
convex dominating set,convex domination number,convex domination subdivision number
http://comb-opt.azaruniv.ac.ir/article_13544.html
http://comb-opt.azaruniv.ac.ir/article_13544_b044108d0b0eedf90a89cf1f47c4f8e0.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
1
2016
08
10
More skew-equienergetic digraphs
57
73
EN
Ch.
Adiga
University of Mysore
c_adiga@hotmail.com
Rakshith
B R
University of Mysore
ranmsc08@yahoo.co.in
10.22049/cco.2016.13545
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.
energy of a graph,skew energy of a digraph,equienergetic graphs,skew-equienergetic digraphs
http://comb-opt.azaruniv.ac.ir/article_13545.html
http://comb-opt.azaruniv.ac.ir/article_13545_0f42ad1856ecb7c77844ab63bd68ed35.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
1
2016
06
01
Bounds on the restrained Roman domination number of a graph
75
82
EN
H.
Abdollahzadeh Ahangar
Babol Noshirvani University of Technology
ha.ahangar@yahoo.com
S.R.
Mirmehdipour
Babol Noshirvani University of Technology
r.m.mehdipor@gmail.com
10.22049/cco.2016.13556
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.
Roman dominating function,Roman domination number,restrained Roman dominating function,restrained Roman domination number
http://comb-opt.azaruniv.ac.ir/article_13556.html
http://comb-opt.azaruniv.ac.ir/article_13556_af7da9ddc41c8343edb4835aaab47c2c.pdf