Deciding Graph non-Hamiltonicity via a Closure Algorithm
E. R.
Swart
Kelowna, British Columbia, Canada
author
Stephen J.
Gismondi
University of Guelph, Canada
author
N. R.
Swart
University of British Columbia Okanagan, Canada
author
C. E.
Bell
Guelph, Ontario, Canada
author
A.
Lee
University of Guelph, Canada
author
text
article
2016
eng
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
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
1
35
https://jac.ut.ac.ir/article_7937_15545482e67a30452c97e86eb5b51fa9.pdf
On the tenacity of cycle permutation graph
D.
Jelodar
University of Tehran, Department of Algorithms and Computation
author
D.
Moazzami
University of Tehran, College of Engineering, Department of Engineering Science
author
P.
Nasehpour
University of Tehran, College of Engineering, Department of Engineering Science
author
text
article
2016
eng
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.
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
37
44
https://jac.ut.ac.ir/article_7938_a7b34f56efc535ed46a94f44aa7e3d23.pdf
A note on 3-Prime cordial graphs
R.
Ponraj
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627412, India
author
Rajpal
Singh
Research Scholar, Department of Mathematics Manonmaniam Sundaranar University, Tirunelveli-627012, India
author
S.
Sathish Narayanan
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627412, India
author
text
article
2016
eng
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.
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
45
55
https://jac.ut.ac.ir/article_7939_495c61efe2289c038edc6c7099386507.pdf
Edge pair sum labeling of some cycle related graphs
P.
Jeyanthi
Govindammal Aditanar College for Women Tiruchendur-628 215, Tamil Nadu, India
author
T.
Saratha Devi
Department of Mathematics, G.Venkataswamy Naidu College, Kovilpatti-628502,Tamilnadu,India.
author
text
article
2016
eng
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, <Cm,K1,n> and <Cm * K1,n> admit edge pair sum labeling.
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
57
68
https://jac.ut.ac.ir/article_7940_56568b68b988fc59429af15e748b7a64.pdf
4-Prime cordiality of some classes of graphs
R.
Ponraj
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India
author
Rajpal
Singh
Research Scholar, Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli-627012, India
author
S.
Sathish Narayanan
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India
author
A. M. S.
Ramasamy
Department of Mathematics, Vel Tech Dr.R.R & Dr.S.R Technical University, Chennai-600002, India
author
text
article
2016
eng
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.
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
69
79
https://jac.ut.ac.ir/article_7941_01050790c89557f0425ee26385c3b6b9.pdf
Further results on odd mean labeling of some subdivision graphs
R.
Vasuki
Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215, Tamil Nadu, India
author
S.
Suganthi
Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215, Tamil Nadu, India
author
G.
Pooranam
Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215, Tamil Nadu, India
author
text
article
2016
eng
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..
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
81
98
https://jac.ut.ac.ir/article_7942_b5919c4f284019e6cc358136ade4b8ed.pdf
An Optimization Model for Epidemic Mitigation and Some Theoretical and Applied Generalizations
Sima
Ranjbarfard
Department of Algorithms and Computation, University of Tehran.
author
Amin
Ghodousian
University of Tehran, College of Engineering, Faculty of Engineering Science
author
D.
Moazzami
University of Tehran, College of Engineering, Faculty of Engineering Science
author
text
article
2016
eng
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.
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
99
116
https://jac.ut.ac.ir/article_7945_d579d657e55fe3023b8855e49200e683.pdf
Constructing Graceful Graphs with Caterpillars
Christian
Barrientos
Department of Mathematics, Clayton State University, Morrow, Georgia 30260, USA
author
Sarah
Minion
Department of Mathematics, Clayton State University, Morrow, Georgia 30260, USA
author
text
article
2016
eng
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.
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
117
125
https://jac.ut.ac.ir/article_7946_ab86e4c77cafca0ee7fc0724a85925bb.pdf
Total vertex irregularity strength of corona product of some graphs
P.
Jeyanthi
Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628 215, Tamil Nadu, India.
author
A.
Sudha
Department of Mathematics, Wavoo Wajeeha Women’s College of Arts and Science, Kayalpatnam -628 204,Tamil Nadu, India.
author
text
article
2016
eng
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
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
127
140
https://jac.ut.ac.ir/article_7948_75d3525b3126762d9d4dfccb440cd4e7.pdf
A Survey on Stability Measure of Networks
Peyman
Nasehpour
Department of Algorithms and Computation, Faculty of Engineering Science, University of Tehran
author
text
article
2016
eng
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.
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
141
148
https://jac.ut.ac.ir/article_7952_6f002c9f5ab6a9706c13862fae8bd92a.pdf
Towards a measure of vulnerability, tenacity of a Graph
Dara
Moazzami
University of Tehran, College of Engineering, Department of Engineering Science
author
text
article
2016
eng
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.
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
149
153
https://jac.ut.ac.ir/article_7953_f2b13c1826d752109b66c0748d01a288.pdf
A Survey On the Vulnerability Parameters of Networks
Mahmood
Shabankhah
University of Tehran, College of Engineering, Faculty of Engineering Science
author
text
article
2016
eng
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.
Journal of Algorithms and Computation
University of Tehran
2476-2776
48
v.
1
no.
2016
155
162
https://jac.ut.ac.ir/article_7955_90bffa8a1a1619f646beb2bd9af65d54.pdf