in this paper, we obtain the general solution and the generalized  hyers--ulam--rassias stability in random normed spaces, in non-archimedean spacesand also in $p$-banach spaces and finally the stability viafixed point method for a functional equationbegin{align*}&d_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1...

Let G be a strongly connected digraph, and dG(vi,vj) denote the distance from vertex vi to vj defined as length of shortest directed path in G. The sum between vertices is sdG(vi,vj)=dG(vi,vj)+dG(vj,vi). matrix n×n SD(G)=(sdG(vi,vj))vi,vj∈V(G). For vi∈V(G), transmission G, denoted by STG(vi) or STi, row SD(G) corresponding vi. ST(G)=diag(ST1,ST2,…,STn) diagonal with transmissions zeroes elsewhe...