A. Khodkar

activity

20142021

most citedDifference Covering Arrays and Pseudo-Orthogonal Latin Squares

12 citations · 32 across the 14 of their papers we have counts for

collaborators

14 papers

math.CO2021

Signed Magic arrays with certain property

Chanceley Book, Abdollah Khodkar

A signed magic array, $S M A (m, n; s, t)$ , is an $m \times n$ array with the same number of filled cells $s$ in each row and the same number of filled cells $t$ in each column, filled…

math.CO2020★ 7 cited

Covering Italian domination in graphs

Abdollah Khodkar, Doost Ali Mojdeh, Babak Samadi +1

For a graph $G = (V (G), E (G))$ , an Italian dominating function (ID function) of $G$ is a function $f : V (G) \to {0, 1, 2}$ such that for each vertex $v \in V (G)$ with $f (v) = 0$ , $f…

math.CO2019★ 4 cited

Signed magic rectangles with three filled cells in each column

Abdollah Khodkar, David Leach, Brandi Ellis

A {\em signed magic rectangle} $S M R (m, n; k, s)$ is an $m \times n$ array with entries from $X$ , where $X = {0, \pm 1, \pm 2, \dots,$ $\pm (mk - 1) /2}$ if $mk$ is odd and $X = \{\pm1,\pm2…

math.CO2019★ 1 cited

Total dominator coloring of circulant graphs $C_{n} (a, b)$

Adel P. Kazemi, Parvin Jalilolghadr, Abdollah Khodkar

The circulant graph $C_{n} (S)$ with connection set $S \subseteq {1, 2, \dots, n}$ is the graph with vertex set $V = {1, \dots, n}$ and two vertices $x, y$ are adjacent if $∣ x - y ∣ \in S$ .…

math.CO2019★ 1 cited

Signed magic rectangles with two filled cells in each column

Abdollah Khodkar, Brandi Ellis

A signed magic rectangle $S M R (m, n; r, s)$ is an $m \times n$ array with entries from $X$ , where $X = {0, \pm 1, \pm 2, \dots,$ $\pm (m s - 1) /2}$ if $m r$ is odd and $X = \{\pm1,\pm2,\ldot…

math.CO2018★ 1 cited

Magic rectangles with empty cells

Abdollah Khodkar, David Leach

A magic rectangle of order $m \times n$ with precisely $r$ filled cells in each row and precisely $s$ filled cells in each column, denoted $M R (m, n; r, s)$ , is an arrangement of the nu…

math.CO2018★ 3 cited

Magic squares with empty cells

Abdollah Khodkar, David Leach

A k-magic square of order n is an arrangement of the numbers from 0 to kn-1 in an n by n matrix, such that each row and each column has exactly k filled cells, each number occurs e…

math.CO2017

Signed edge domination numbers of complete tripartite graphs: Part 2

Abdollah Khodkar

The closed neighborhood $N_{G} [e]$ of an edge $e$ in a graph $G$ is the set consisting of $e$ and of all edges having an end-vertex in common with $e$ . Let $f$ be a function on $E(G)…

math.CO2017

Existence of Some Signed Magic Arrays

Abdollah Khodkar, Christian Schulz, Nathan Wagner

We consider the notion of a signed magic array, which is an $m \times n$ rectangular array with the same number of filled cells $s$ in each row and the same number of filled cells…

math.CO2015

$(r)$ -Pancyclic, $(r)$ -Bipancyclic and Oddly $(r)$ -Bipancyclic Graphs

Abdollah Khodkar, Oliver Sawin, Lisa Mueller +1

A graph with $v$ vertices is $(r)$ -pancyclic if it contains precisely $r$ cycles of every length from 3 to $v$ . A bipartite graph with even number of vertices $v$ is said to be $(r…

math.CO2015★ 12 cited

Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

Fatih Demirkale, Diane M. Donovan, Joanne Hall +2

Difference arrays are used in applications such as software testing, authentication codes and data compression. Pseudo-orthogonal Latin squares are used in experimental designs. A…

math.CO2014

$(k, k^{'}, k^{''})$ -domination in graphs

Abdollah Khodkar, Babak Samadi, H. R. Golmohammadi

We first introduce the concept of (k,k',k'')-domination numbers in graphs, which is a generalization of many domination parameters. Then we find lower and upper bounds for this par…

math.CO2014★ 3 cited

New bounds on the signed domination numbers of graphs

S. M. Hosseini Moghaddam, Abdollah Khodkar, Babak Samadi

In this paper, we study the signed domination numbers of graphs and present new sharp lower and upper bounds for this parameter. As an example, we present a lower bound on signed d…