  Any graph can be considered as a network of resistors, each of which has a
resistance of $1 \Omega.$ The resistance distance $r_{ij}$ between a pair of
vertices $i$ and $j$ in a graph is defined as the effective resistance between
$i$ and $j$. This article deals with the resistance distance in the
$k$-coalescence of complete graphs. We also present its results in connection
with the Kemeny's constant, Kirchhoff index, additive degree-Kirchhoff index,
multiplicative degree-Kirchhoff index and mixed degree-Kirchhoff index.
Moreover, we obtain the resistance distance in the $k$-coalescence of a
complete graph with particular graphs. As an application, we provide the
resistance distance of certain graphs such as the vertex coalescence of a
complete bipartite graph with a complete graph, a complete bipartite graph with
a star graph, the windmill graph, pineapple graph, etc.

Combinatorics