Spanning Integrity for Signed Fuzzy Graphs

The integrity parameter relates a set of vertices and other disconnected components. For improved connectivity, a vulnerability parameter should address the relation between all vertices. Spanning integrity encourages all the vertices to be connected by means of spanning. In this paper, the vulnerability parameter spanning integrity is introduced, for the signed fuzzy graph (SFG). The parameter is defined and explained with some examples. The spanning integrity is determined for standard SFGs, such as star SFG, complete SFG, bipartite SFG and complete bipartite SFG. Operations on SFGs are discussed. Spanning integrity is calculated for union, join, and Cartesian products of SFG. An algorithm is presented to compute the spanning integrity of SFG. This algorithm is validated by practical application in air networks. It helps to find the best route and to overcome the complicated connection between destinations while implementing a new air project, in a simple manner.