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Changing and Unchanging the Signal Number: Edge Removal

55 DOI: 10.37398/JSR.2021.650908 Abstract -: For two vertices u and v in a connected graph G, the signal distance dSD (u, v) from u to v is defined by dSD (u, v) = minS{d(u,v) +∑w∈V(G) (deg w 2)+(deg u 1) + (deg v − 1)},where S is a path connecting u and v, d(u, v) is the length of the path S and in the sum ∑w∈V (G) runs over all the internal vertices between u and v in the path S. A path between the vertices u and v of length dSD (u, v) is called a u − v geosig path. A set S ⊆ V is called a signal set, if every vertex x in G lies on a geosig path joining a pair of vertices of S. This paper, we study about the criticality and stability of the signal number after removing an edge from a graph.