Counting independent dominating sets in linear polymers
S. Alikhani, S. Jahari
A vertex subset W ⊆ V of the graph G = (V, E) is an independent dominating set,
if every vertex in V \ W is adjacent to at least one vertex in W and the vertices of W are pairwise non-adjacent.
We enumerate independent dominating sets in several classes
of graphs (polymer graph) made by a linear or cyclic concatenation of basic building blocks. Explicit recurrences are derived for the number of
independent dominating sets of these kind of graphs. Generating functions for the
number of independent dominating sets of triangular and squares cacti chain are also computed.
Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16, supplement issue 1 (2023), pp. 47-57
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