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} defi ned 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,...,±kp/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} defi ned 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 prespeci ed 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 di erence 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 di erent 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