2 papers
math.CO2026
On the Roots of Connected Domination Polynomials
Pingping Shao, Chengye Zhao
We determine the closure of the connected domination roots. The main tool is a substitution formula for the lexicographic product with a complete graph, $D_c(G[K_n],x)=D_c(G,(x+1)^…
math.CO2026
Counting Weight- Italian Dominating Sets on Trees and Cycles
Pingping Shao, Chengye Zhao
We study the problem of counting \emph{Italian dominating functions} (IDFs) of each possible weight on paths, trees, and cycles. An Italian dominating function on a graph …