Annammal Arputhamary - Academia.edu (original) (raw)
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Papers by Annammal Arputhamary
2021 International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT), 2021
Security is the primary concern for decades in networking and still face enormous challenges. Def... more Security is the primary concern for decades in networking and still face enormous challenges. Defending a network against attacks on its nodes requires placing mobile guards on the nodes of a network. The meshes and n-cubes are one of the most versatile and powerful interconnection networks and are bipartite. In this paper, the exact value of the parameter which gives the minimum number of guards required to protect the n-cubes and meshes is obtained. The n-cubes and mesh structures constitute the basic unit of nano networks. The main theme of this proposed study is the security of interconnected networks.
2021 5th International Conference on Computing Methodologies and Communication (ICCMC), 2021
Locating defective elements in a processor network brings the motivation for location dominating ... more Locating defective elements in a processor network brings the motivation for location dominating sets. In this paper, the location dominating set problem for friendship graphs is solved. Location problems examine the ability to pinpoint the origin of an event. Friendship graphs are used to analyze social networks. Domination in social networks is used to find the most powerful node in such networks and location domination is significant in locating the faulty or the unusable node in that network.
Let G be an undirected simple graph. A strong edge coloring of a graph G is a function f : E → {1... more Let G be an undirected simple graph. A strong edge coloring of a graph G is a function f : E → {1, 2, . . . , k} such that f(e1) 6= f(e2) whenever e1 and e2 lie within distance 2 from each other. In other words, no two edges lie on a path of length 3 receive same colors. The smallest number of colors essential for strong edge coloring of a graph G is entitled as strong chromatic index and is represented by χs(G). In this paper, we investigate strong chromatic index of some classes of unicyclic graphs. MSC: 05C15, 05C40.
2021 6th International Conference on Inventive Computation Technologies (ICICT), 2021
An edge colored graph is properly colored if there exists a proper path (a path in which two neig... more An edge colored graph is properly colored if there exists a proper path (a path in which two neighboring edges do not acquire identical color) amid every two distinct vertices. Such a graph is called a properly connected graph and such a coloring of the graph G is called a properly connected coloring. The proper connection number of G is the least number of colors essential for a properly connected coloring of G and is symbolized as pc(G). The strong proper connection number, represented by spc(G) is the least possible number of colors necessary to color the edges of G so that amid every two vertices, there is a shortest proper path. In this article, graphs with equal proper connection numbers and strong proper connection have been investigated.
Advances in Mathematics: Scientific Journal, 2020
International Journal of Mathematical Analysis, 2017
A path in a vertex-colored graph G is called a rainbow path if no two internal vertices get the s... more A path in a vertex-colored graph G is called a rainbow path if no two internal vertices get the same color. A vertex-colored graph G is strongly rainbow vertexconnected, if for every pair of distinct vertices, there exists at least one shortest rainbow path. The minimum number of colors required to strongly rainbow vertex color a graph G is called the strong rainbow vertex-connection number, denoted by srvc(G) .This work presents the exact values of strong rainbow vertexconnection numbers for the generalized Petersen graphs G(n,2) and G(n,3) .
Wireless Personal Communications, 2016
A strong edge coloring of a graph G is a proper edge coloring in which no two edges of the same c... more A strong edge coloring of a graph G is a proper edge coloring in which no two edges of the same color lie within distance 2 from each other. The minimum number of colors required for strong edge coloring of a graph G is called strong chromatic index and is denoted by \chi _{s}^{\prime } (G)$$χs′(G). Channel assignment problems are closely related with strong edge coloring problem where the colors represent frequencies. In wireless networks, assigning channels or frequencies to the links between transceivers (vertices) to avoid interference can be modelled as a strong edge coloring problem. In this paper, we determine the exact values of strong chromatic indices of interconnection networks namely butterfly network, Benes network, hypertree network and honeycomb network.
Procedia Computer Science, 2015
2016 Online International Conference on Green Engineering and Technologies (IC-GET), 2016
Decompositions play a vital role in graph theory. It provides an efficient method to partition th... more Decompositions play a vital role in graph theory. It provides an efficient method to partition the edges of Gso that the results for complicated graphs can be achieved by means of its subgraphs. We show how to find the minimum number of colours required in an edge colouring of a connected graphGin which every pair of vertices is connected by at least one shortest path in which no two edges are coloured the same using subgraph decomposition. In this paper, we compute the strong rainbow edge-connection number using A-decomposition for some classes of snake graphs and Sierpinski triangle graph.
2015 IEEE 9th International Conference on Intelligent Systems and Control (ISCO), 2015
The rainbow vertex - connection number, rvc(G), of a connected graph is the minimum number of col... more The rainbow vertex - connection number, rvc(G), of a connected graph is the minimum number of colors needed to color its vertices such that every pair of vertices is connected by at least one path whose internal vertices have distinct colors. Rainbow coloring has received much attention recently in the field of interconnection networks. Computing the rainbow connection number of a graph is NP- hard and it finds its applications in the secure transfer of classified information between agencies and in cellular network. In this paper we characterize some families of cubic graphs and its strong rainbow connection numbers have been found.
Procedia Computer Science
2021 International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT), 2021
Security is the primary concern for decades in networking and still face enormous challenges. Def... more Security is the primary concern for decades in networking and still face enormous challenges. Defending a network against attacks on its nodes requires placing mobile guards on the nodes of a network. The meshes and n-cubes are one of the most versatile and powerful interconnection networks and are bipartite. In this paper, the exact value of the parameter which gives the minimum number of guards required to protect the n-cubes and meshes is obtained. The n-cubes and mesh structures constitute the basic unit of nano networks. The main theme of this proposed study is the security of interconnected networks.
2021 5th International Conference on Computing Methodologies and Communication (ICCMC), 2021
Locating defective elements in a processor network brings the motivation for location dominating ... more Locating defective elements in a processor network brings the motivation for location dominating sets. In this paper, the location dominating set problem for friendship graphs is solved. Location problems examine the ability to pinpoint the origin of an event. Friendship graphs are used to analyze social networks. Domination in social networks is used to find the most powerful node in such networks and location domination is significant in locating the faulty or the unusable node in that network.
Let G be an undirected simple graph. A strong edge coloring of a graph G is a function f : E → {1... more Let G be an undirected simple graph. A strong edge coloring of a graph G is a function f : E → {1, 2, . . . , k} such that f(e1) 6= f(e2) whenever e1 and e2 lie within distance 2 from each other. In other words, no two edges lie on a path of length 3 receive same colors. The smallest number of colors essential for strong edge coloring of a graph G is entitled as strong chromatic index and is represented by χs(G). In this paper, we investigate strong chromatic index of some classes of unicyclic graphs. MSC: 05C15, 05C40.
2021 6th International Conference on Inventive Computation Technologies (ICICT), 2021
An edge colored graph is properly colored if there exists a proper path (a path in which two neig... more An edge colored graph is properly colored if there exists a proper path (a path in which two neighboring edges do not acquire identical color) amid every two distinct vertices. Such a graph is called a properly connected graph and such a coloring of the graph G is called a properly connected coloring. The proper connection number of G is the least number of colors essential for a properly connected coloring of G and is symbolized as pc(G). The strong proper connection number, represented by spc(G) is the least possible number of colors necessary to color the edges of G so that amid every two vertices, there is a shortest proper path. In this article, graphs with equal proper connection numbers and strong proper connection have been investigated.
Advances in Mathematics: Scientific Journal, 2020
International Journal of Mathematical Analysis, 2017
A path in a vertex-colored graph G is called a rainbow path if no two internal vertices get the s... more A path in a vertex-colored graph G is called a rainbow path if no two internal vertices get the same color. A vertex-colored graph G is strongly rainbow vertexconnected, if for every pair of distinct vertices, there exists at least one shortest rainbow path. The minimum number of colors required to strongly rainbow vertex color a graph G is called the strong rainbow vertex-connection number, denoted by srvc(G) .This work presents the exact values of strong rainbow vertexconnection numbers for the generalized Petersen graphs G(n,2) and G(n,3) .
Wireless Personal Communications, 2016
A strong edge coloring of a graph G is a proper edge coloring in which no two edges of the same c... more A strong edge coloring of a graph G is a proper edge coloring in which no two edges of the same color lie within distance 2 from each other. The minimum number of colors required for strong edge coloring of a graph G is called strong chromatic index and is denoted by \chi _{s}^{\prime } (G)$$χs′(G). Channel assignment problems are closely related with strong edge coloring problem where the colors represent frequencies. In wireless networks, assigning channels or frequencies to the links between transceivers (vertices) to avoid interference can be modelled as a strong edge coloring problem. In this paper, we determine the exact values of strong chromatic indices of interconnection networks namely butterfly network, Benes network, hypertree network and honeycomb network.
Procedia Computer Science, 2015
2016 Online International Conference on Green Engineering and Technologies (IC-GET), 2016
Decompositions play a vital role in graph theory. It provides an efficient method to partition th... more Decompositions play a vital role in graph theory. It provides an efficient method to partition the edges of Gso that the results for complicated graphs can be achieved by means of its subgraphs. We show how to find the minimum number of colours required in an edge colouring of a connected graphGin which every pair of vertices is connected by at least one shortest path in which no two edges are coloured the same using subgraph decomposition. In this paper, we compute the strong rainbow edge-connection number using A-decomposition for some classes of snake graphs and Sierpinski triangle graph.
2015 IEEE 9th International Conference on Intelligent Systems and Control (ISCO), 2015
The rainbow vertex - connection number, rvc(G), of a connected graph is the minimum number of col... more The rainbow vertex - connection number, rvc(G), of a connected graph is the minimum number of colors needed to color its vertices such that every pair of vertices is connected by at least one path whose internal vertices have distinct colors. Rainbow coloring has received much attention recently in the field of interconnection networks. Computing the rainbow connection number of a graph is NP- hard and it finds its applications in the secure transfer of classified information between agencies and in cellular network. In this paper we characterize some families of cubic graphs and its strong rainbow connection numbers have been found.
Procedia Computer Science