R. Revathi ¹, R. Rajeswari ¹

Affiliations
1 Department of Mathematics, Sathyabama University, Chennai 600119, IN

Abstract

A graph G (V,E) with |V| = n is said to have modular multiplicative divisor labeling if there exist a bijection f: V(G) → {1, 2, …,} and the induced function f^*: E(G) → {0, 1, 2, …, n - 1} where f(uv) = f(u)f(v) (mod n) such that n divides the sum of all edge labels of G. We prove that the path P_n , and the graph P_{a, b} (a graph which connects two vertices by means of "b" internally disjoint paths of length "a" each), shadow graph of a path and the cartesian product P_n × P₁, (n is not a multiple of 6) admits modular multiplicative divisor labeling. Also we discuss the upper bound for the number of edges in a modular multiplicative divisor graphs. AMS Subject Classification: 05C78

Keywords

Graph Labeling, Path, Graph P_a,b, Shadow Graph D₂(G), the Cartesian Product P_n × P₁

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R. Ambika ¹, R. Rajeswari ², A. Nivedita ³

Affiliations
1 Department of Electrical Engineering Sri Krishna College of Technology, Coimbatore, IN
2 Department of Electrical Engineering, Government College of Technology, Coimbatore, IN
3 Sri Krishna College of Technology, Coimbatore, IN

Abstract

Reactive power optimization is one of the efficient ways of improving power system reliability and efficiency which is beneficial in power planning studies. ORPD problems are best solved using different algorithms to achieve optimization. This paper deals a comparative study of three algorithms PSO, GSA and hybrid PSOGSA algorithm. The ORPD multiobjective problem is tested over standard IEEE system. The test is performed under two conditions with and without penalty function added to the objective function. And all results obtained are summarized and best optimal solution is obtained from the hybrid PSOGSA algorithm.

Keywords

ORPD (Optimal Reactive Power Dispatch) Problem, GSA (Gravitational Search algorithm), PSO (Particle swarm Optimization), Hybrid PSOGSA.

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R. Thamizharasi ¹, R. Rajeswari ¹

Affiliations
1 Sathyabama University, Chennai – 600119, Tamil Nadu, IN

Abstract

Objectives: In this paper, we prove that the line digraphs of Cayley digraphs admit super vertex (a,d) antimagic labeling, product anti magic and vertex magic total labeling. Also we have shown the labeling formula to get the same. Findings: If a Cayley digraph admits the above three labelings, then the line digraph of Cayley digraph also admits the same.

Keywords

Antimagic, Labelings, Line Digraphs, Magic.

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