2017
49
1
0
0
Theta Graph Designs
2
2
We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges.
1

1
16


Anthony D.
Forbes
Department of Mathematics and Statistics, The Open University, Milton Keynes MK7 6AA,
UK.
Department of Mathematics and Statistics,
Iran
anthony.d.forbes@gmail.com


Terry S.
Griggs
Department of Mathematics and Statistics, The Open University, Milton Keynes MK7 6AA,
UK.
Department of Mathematics and Statistics,
Iran
terry.griggs@open.ac.uk


Tamsin J.
Forbes
22 St Albans Road, Kingston upon Thames KT2 5HQ, UK
22 St Albans Road, Kingston upon Thames KT2
Iran
tamsin.forbes@gmail.com
Graph design
Graph decomposition
Theta graph
Remainder Cordial Labeling of Graphs
2
2
In this paper we introduce remainder cordial labeling of graphs. Let $G$ be a $(p,q)$ graph. Let $f:V(G)rightarrow {1,2,...,p}$ be a $11$ map. For each edge $uv$ assign the label $r$ where $r$ is the remainder when $f(u)$ is divided by $f(v)$ or $f(v)$ is divided by $f(u)$ according as $f(u)geq f(v)$ or $f(v)geq f(u)$. The function$f$ is called a remainder cordial labeling of $G$ if $left e_{f}(0)  e_f(1) rightleq 1$ where $e_{f}(0)$ and $e_{f}(1)$ respectively denote the number of edges labelled with even integers and odd integers. A graph $G$ with a remainder cordial labeling is called a remainder cordial graph. We investigate the remainder cordial behavior of path, cycle, star, bistar, crown, comb, wheel, complete bipartite $K_{2,n}$ graph. Finally we propose a conjecture on complete graph $K_{n}$.
1

17
30


R.
Ponraj
Department of Mathematics, Sri Paramakalyani College, Alwarkurichi{627 412, India
Department of Mathematics, Sri Paramakalyani
Iran
ponrajmaths@gmail.com


K.
Annathurai
Department of Mathematics, Thiruvalluvar College,, Papanasam{627 425, India
Department of Mathematics, Thiruvalluvar
Iran
kanathuraitvcmaths@gmail.com


R.
Kala
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli{ 627 012,
India.
Department of Mathematics, Manonmaniam Sundaranar
Iran
karthipyi91@yahoo.co.in
vertex equitable labeling
vertex Path
Cycle
Star
Bistar
Crown
Comb
wheel
complete bipartite graph
complete graph graph
Asteroidal number for some product graphs
2
2
The notion of Asteroidal triples was introduced by Lekkerkerker and Boland [6]. D.G.Corneil and others [2], Ekkehard Kohler [3] further investigated asteroidal triples. Walter generalized the concept of asteroidal triples to asteroidal sets [8]. Further study was carried out by Haiko Muller [4]. In this paper we find asteroidal numbers for Direct product of cycles, Direct product of path and cycle, Strong product of paths and cycles and some more graphs.
1

31
43


S.
ALAGU
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli  627 012, Tamilnadu, India
Department of Mathematics, Manonmaniam Sundaranar
Iran
alagu391@gmail.com


R.
KALA
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli  627 012, Tamilnadu, India
Department of Mathematics, Manonmaniam Sundaranar
Iran
karthipyi91@yahoo.co.in
vertex equitable labeling
Asteroidal number
asteroidal sets
independence number
cartesian product
Edgetenacity in Networks
2
2
Numerous networks as, for example, road networks, electrical networks and communication networks can be modeled by a graph. Many attempts have been made to determine how well such a network is "connected" or stated differently how much effort is required to break down communication in the system between at least some nodes. Two wellknown measures that indicate how "reliable" a graph is are the "Tenacity" and "Edgetenacity" of a graph. In this paper we present results on the tenacity and edgetenacity, $T_e(G)$, a new invariant, for several classes of graphs. Basic properties and some bounds for edgetenacity, $T_e(G)$, are developed. Edgetenacity values for various classes of graphs are calculated and future work andconcluding remarks are summarized
1

45
53


Dara
Moazzami
University of Tehran, College of Engineering, Department of Engineering Science
University of Tehran, College of Engineering,
Iran
dmoazzami@ut.ac.ir
Edgetenacity
network vulnerability
Linear optimization on the intersection of two fuzzy relational inequalities defined with Yager family of tnorms
2
2
In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Yager family of tnorms is considered as fuzzy composition. Yager family of tnorms is a parametric family of continuous nilpotent tnorms which is also one of the most frequently applied one. This family of tnorms is strictly increasing in its parameter and covers the whole spectrum of tnorms when the parameter is changed from zero to infinity. The resolution of the feasible region of the problem is firstly investigated when it is defined with maxYager composition. Based on some theoretical results, conditions are derived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented. It is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. A method is proposed to generate random feasible maxYager fuzzy relational inequalities and an algorithm is presented to solve the problem. Finally, an example is described to illustrate these algorithms
1

55
82


Amin
Ghodousian
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 113654563, Tehran, Iran
Faculty of Engineering Science, College of
Iran
a.ghodousian@ut.ac.ir


Reza
Zarghani
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, 111554563, Iran
School of Mechanical Engineering, College
Iran
rezazarghani@ut.ac.ir
Fuzzy relation
fuzzy relational inequality
linear optimization
fuzzy compositions and tnorms
Tenacity and some related results
2
2
Conceptually graph vulnerability relates to the study of graphintactness when some of its elements are removed. The motivation forstudying vulnerability measures is derived from design and analysisof networks under hostile environment. Graph tenacity has been anactive area of research since the the concept was introduced in1992. The tenacity T(G) of a graph G is defined asbegin{center} $T(G)=displaystyle min_{Asubset V(G)}{frac{mid Amid +tau(GA)}{omega(GA)}}$end{center}where $tau(GA)$ denotes the order (the number of vertices) of alargest component of GA and $omega(GA)$ is the number ofcomponents of GA. In this paper we discuss tenacity and its properties invulnerability calculation.
1

83
91


Dara
Moazzami
University of Tehran, College of Engineering, Department of Engineerng Science
University of Tehran, College of Engineering,
Iran
dmoazzami@ut.ac.ir
vertex connectivity
toughness
binding number
independence number
edgeconnectivity
An improved algorithm to reconstruct a binary tree from its inorder and postorder traversals
2
2
It is wellknown that, given inorder traversal along with one of the preorder or postorder traversals of a binary tree, the tree can be determined uniquely. Several algorithms have been proposed to reconstruct a binary tree from its inorder and preorder traversals. There is one study to reconstruct a binary tree from its inorder and postorder traversals, and this algorithm takes running time of $ BigO{emph{n}^2} $. In this paper, we present $ proc{InPos} $ an improved algorithm to reconstruct a binary tree from its inorder and postorder traversals. The running time and space complexity of the algorithm are an order of $ BigTheta{emph{n}} $ and $ BigTheta{emph{n}} $ respectively, which we prove to be optimal. The $ proc{InPos} $ algorithm not only reconstructs the binary tree, but also it determines different types of the nodes in a binary tree; nodes with two children, nodes with one child, and nodes with no child. At the end, the $ proc{InPos} $ returns a matrixbased structure to represent the binary tree, and enabling access to any structural information of the reconstructed tree in linear time with any given tree traversals.
1

93
113


Niloofar
Aghaieabiane
Department of Engineering, School of Computer Science, New Jersey Institute of Technology, Newark, New Jersey, the USA.
Department of Engineering, School of Computer
Iran
na396@njit.edu


Henk
Koppelaar
Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands.
Faculty of Electrical Engineering, Mathematics
Iran
koppelaar.henk@gmail.com


Peyman
Nasehpour
Golpayegan University of Technology, Department of Engineering Science, Golpayegan, Iran.
Golpayegan University of Technology, Department
Iran
nasehpour@gut.ac.ir, nasehpour@gmail.com
Binary tree
Preorder traversal
Inorder traversal
Postorder traversal
Time complexity
Space complexity
Linear optimization on Hamacherfuzzy relational inequalities
2
2
In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Hamacher family of tnorms is considered as fuzzy composition. Hamacher family of tnorms is a parametric family of continuous strict tnorms, whose members are decreasing functions of the parameter. The resolution of the feasible region of the problem is firstly investigated when it is defined with maxHamacher composition. Based on some theoretical results, a necessary and sufficient condition and three other necessary conditions are derived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented. It is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. A method is proposed to generate random feasible maxHamacher fuzzy relational inequalities and an algorithm is presented to solve the problem. Finally, an example is described to illustrate these algorithms.
1

115
150


Amin
Ghodousian
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 113654563, Tehran, Iran
Faculty of Engineering Science, College of
Iran
a.ghodousian@ut.ac.ir


Mohammadsadegh
Nouri
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 113654563, Tehran, Iran.
Faculty of Engineering Science, College of
Iran
msadegh$\_$nouri@ut.ac.ir
Fuzzy relation
fuzzy relational inequality
linear optimization
fuzzy compositions and tnorms