Let G=Kn1β,n2β,β―,ntββ be a complete t-partite graph on
n=βi=1tβniβ vertices. The distance between vertices i and j in
G, denoted by dijβ is defined to be the length of the shortest path
between i and j. The squared distance matrix Ξ(G) of G is the
nΓn matrix with (i,j)th entry equal to 0 if i=j and equal to
dij2β if iξ =j. We define the squared distance energy EΞβ(G)
of G to be the sum of the absolute values of its eigenvalues. We determine
the inertia of Ξ(G) and compute the squared distance energy
EΞβ(G). More precisely, we prove that if niββ₯2 for 1β€iβ€t, then EΞβ(G)=8(nβt) and if h=β£{i:niβ=1}β£β₯1, then
8(nβt)+2(hβ1)β€EΞβ(G)<8(nβt)+2h. Furthermore, we show that
for a fixed value of n and t, both the spectral radius of the squared
distance matrix and the squared distance energy of complete t-partite graphs
on n vertices are maximal for complete split graph Sn,tβ and minimal for
Tur{\'a}n graph Tn,tβ