Advances and Applications in Discrete Mathematics © 2020 Pushpa Publishing House, Prayagraj, India http://www.pphmj.com http://dx.doi.org/10.17654/DM024020129 Volume 24, Number 2, 2020, Pages 129-142 ISSN: 0974-1658 Received: March 4, 2020; Accepted: June 5, 2020 2010 Mathematics Subject Classification: 05C22, 91D30. Keywords and phrases: signed graph, switching, switching isomorphism, frustration index, frustration number. SIGNED COMPLETE GRAPHS ON SIX VERTICES AND THEIR FRUSTRATION INDICES Deepak Sehrawat and Bikash Bhattacharjya Department of Mathematics Indian Institute of Technology Guwahati Guwahati 781039, India e-mail: deepakmath55555@iitg.ac.in b.bikash@iitg.ac.in Abstract A signed graph is a graph whose edges are labeled positive or negative. The sign of a cycle is the product of the signs of its edges. A signed graph is said to be balanced if the sign of every cycle is positive. The frustration index (and frustration number) of a signed graph is the smallest number of edges (and vertices) whose deletion makes the resulting signed graph balanced. In 2012, Zaslavsky [12] proved that upto switching isomorphism, there are six different signed Petersen graphs and he determined the frustration indices (and numbers) of all signed Petersen graphs. In this paper, we determine two things about complete graphs , 6 K with six vertices. First, we determine that there are sixteen signed s, ’ 6 K upto switching isomorphism. Second, we determine the frustration indices and the frustration numbers of all signed s. ’ 6 K