2018-01-19T10:55:07Z
http://jac.ut.ac.ir/?_action=export&rf=summon&issue=48
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
Deciding Graph non-Hamiltonicity via a Closure Algorithm
E. R.
Swart
Stephen J.
Gismondi
N. R.
Swart
C. E.
Bell
A.
Lee
We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the n! Hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices P, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. A graph instance (G) is initially coded as exclusion set E, whose members are pairs of components of P, {pu,i, pv,i+1}, i = 1, n - 1, for each arc (u, v) not in
Hamilton cycle
decision problem
2016
11
28
1
35
http://jac.ut.ac.ir/pdf_371_15545482e67a30452c97e86eb5b51fa9.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
On the tenacity of cycle permutation graph
D.
Jelodar
D.
Moazzami
P.
Nasehpour
A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.
tenacity
Tenacious
Cycle Permutation
toughness
integrity
2016
12
08
37
44
http://jac.ut.ac.ir/pdf_372_a7b34f56efc535ed46a94f44aa7e3d23.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
A note on 3-Prime cordial graphs
R.
Ponraj
Rajpal
Singh
S.
Sathish Narayanan
Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate 3- prime cordial labeling behavior of union of a 3-prime cordial graph and a path Pn.
path
union of graphs
2016
11
10
45
55
http://jac.ut.ac.ir/pdf_373_495c61efe2289c038edc6c7099386507.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
Edge pair sum labeling of some cycle related graphs
P.
Jeyanthi
T.
Saratha Devi
Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or odd. A graph with an edge pair sum labeling is called an edge pair sum graph. In this paper we prove that the graphs GL(n), double triangular snake D(Tn), Wn, Fln, and admit edge pair sum labeling.
Edge pair sum labeling
edge pair sum graph
double triangular snake
wheel graph
ower graph
2016
11
01
57
68
http://jac.ut.ac.ir/pdf_374_56568b68b988fc59429af15e748b7a64.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
4-Prime cordiality of some classes of graphs
R.
Ponraj
Rajpal
Singh
S.
Sathish Narayanan
A. M. S.
Ramasamy
Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate 4- prime cordial labeling behavior of complete graph, book, flower, mCn and some more graphs.
Complete graph
wheel
path
book
flower
2016
12
15
69
79
http://jac.ut.ac.ir/pdf_375_01050790c89557f0425ee26385c3b6b9.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
Further results on odd mean labeling of some subdivision graphs
R.
Vasuki
S.
Suganthi
G.
Pooranam
Let G(V,E) be a graph with p vertices and q edges. A graph G is said to have an odd mean labeling if there exists a function f : V (G) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : E(G) → {1, 3, 5,...,2q - 1} defined by
f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd
is a bijection. A graph that admits an odd mean labeling is called an odd mean graph. In this paper, we have studied an odd meanness property of the subdivision of the slanting ladder SLn for all n ≥ 2; Cn Θ K1 for n ≥ 3; the grid Pm × Pn for m, n ≥ 2; Cm@Cn for m, n ≥ 3 and P2m Θ nK1 for all m, n ≥ 1..
labeling
odd mean labeling
odd mean graph
2016
12
16
81
98
http://jac.ut.ac.ir/pdf_376_b5919c4f284019e6cc358136ade4b8ed.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
An Optimization Model for Epidemic Mitigation and Some Theoretical and Applied Generalizations
Sima
Ranjbarfard
Amin
Ghodousian
D.
Moazzami
In this paper, we present a binary-linear optimization model to prevent the spread of an infectious disease in a community. The model is based on the remotion of some connections in a contact network in order to separate infected nodes from the others. By using this model we nd an exact optimal solution and determine not only the minimum number of deleted links but also their exact positions. The formulation of the model is insensitive to the number of edges in a graph and can be used (with complete or local information) to measure the resistance of a network before and after an infectious spreads. Also, we propose some related models as generalizations: quarantining problem including resource constraints (time, budget, etc.), maximum rescued nodes-minimum deleted links problem and minimum removed links problem nding a prespecied number of nodes with weakest connections.
Epidemic control
Networks
Link removal
Quarantine
Partitioning
Optimization
2016
11
01
99
116
http://jac.ut.ac.ir/pdf_379_d579d657e55fe3023b8855e49200e683.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
Constructing Graceful Graphs with Caterpillars
Christian
Barrientos
Sarah
Minion
A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f is called an -labeling and G is said to be an α-graph. A tree is a caterpillar if the deletion of all its leaves results in a path. In this work we study graceful labelings of the disjoint union of a cycle and a caterpillar. We present necessary conditions for this union to be graceful and, in the case where the cycle has even size, to be an α-graph. In addition, we present a new family of graceful trees constructed using α-labeled caterpillars.
graceful labeling
caterpillar
graceful trees
2016
12
25
117
125
http://jac.ut.ac.ir/pdf_380_ab86e4c77cafca0ee7fc0724a85925bb.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
Total vertex irregularity strength of corona product of some graphs
P.
Jeyanthi
A.
Sudha
A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the total vertex irregularity strength for n ≥ 3, m ≥ 2, Pn ⊙ K1, Pn ⊙ K2, Cn ⊙ K2, Ln ⊙ K1, CLn ⊙ K1, P2 ⊙ Cn, Pn ⊙ Km, Cn ⊙ Km
irregularity strength
total vertex irregularity strength
vertex irregular total labeling
corona product of path and cycle
path and complete graph
ladder and complete graph
graph
2016
12
25
127
140
http://jac.ut.ac.ir/pdf_382_75d3525b3126762d9d4dfccb440cd4e7.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
A Survey on Stability Measure of Networks
Peyman
Nasehpour
In this paper we discuss about tenacity and its properties in stability calculation. We indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. We also give good lower and upper bounds for tenacity.
binding number
connectivity
toughness
tenacity
2016
12
25
141
148
http://jac.ut.ac.ir/pdf_386_59e5788244594db95055102f8978fe03.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
Towards a measure of vulnerability, tenacity of a Graph
Dara
Moazzami
If we think of the graph as modeling a network, the vulnerability measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including connectivity, integrity, toughness, binding number and tenacity.In this paper we discuss tenacity and its properties in vulnerability calculation.
connectivity
integrity
toughness
binding number and tenacity
2016
12
11
149
154
http://jac.ut.ac.ir/pdf_387_7999d7a1346227c73a4872acc73ba654.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2016
48
1
A Survey On the Vulnerability Parameters of Networks
Mahmood
Shabankhah
The analysis of vulnerability in networks generally involves some questions about how the underlying graph is connected. One is naturally interested in studying the types of disruption in the network that maybe caused by failures of certain links or nodes. In terms of a graph, the concept of connectedness is used in dierent forms to study many of the measures of vulnerability. When certain vertices or edges of a connected graph are deleted, one wants to know whether the remaining graph is still connected, and if so, what its vertex - or edge - connectivity is. If on the other hand, the graph is disconnected, the determination of the number of its components or their orders is useful. Our purpose here is to describe and analyze the current status of the vulnerability measures, identify its more interesting variants, and suggesta most suitable measure of vulnerability.
vulnerability measures
connectivity
binding number
toughness
integrity
tenacity
2016
12
25
155
162
http://jac.ut.ac.ir/pdf_389_90bffa8a1a1619f646beb2bd9af65d54.html