Total Domination Polynomial of A Graph

B. Chaluvaraju, V. Chaitra


A total domination polynomial of a graph $G$ of order $n$ is the polynomial $D_{td}(G,x) =\sum^n_{t=\gamma_{td}(G)}d_{td}(G,t)x^t$, where $d_{td}(G,t)$ is the number of total dominating sets of $G$ of cardinality $t$. In this paper, we present various properties of total domination polynomial of graph $G$. Also determine the total domination polynomial of some graph operations.


Graph; Domination number; Sign domination number

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