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Topological invariants are the significant invariants that are used to study the physicochemical and thermodynamic characteristics of chemical compounds. Recently, a new bond additive invariant named the Mostar invariant has been introduced. For any connected graph    ℋ   , the edge Mostar invariant is described asM   o  e    (  ℋ  )   =    ∑   g  x  ∈  E   (  ℋ  )|    m  ℋ    (  g  )   −   m  ℋ    (  x  )    |, wherem  ℋ    (  g  )    (   or    m  ℋ    (  x  )    )is the number of edges of    ℋ    lying closer to vertex  g  (or  x ) than to vertex  x  (or  g ). A graph having at most one common vertex between any two cycles is called a cactus graph. In this study, we compute the greatest edge Mostar invariant for cacti graphs with a fixed number of cycles and  n  vertices. Moreover, we calculate the sharp upper bound of the edge Mostar invariant for cacti graphs inℭ   (   n  ,  s   ), where  s  is the number of cycles.

Edge Mostar Indices of Cacti Graph With Fixed Cycles