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- W2997507220 abstract "Let $G = (V, E)$ be a simple graph of order $n$. A total dominating set of $G$ is a subset $D$ of $V$, such that every vertex of $V$ is adjacent to at least one vertex in $D$. The total domination number of $G$ is minimum cardinality of total dominating set in $G$ and is denoted by $gamma_t(G)$. The total domination polynomial of $G$ is the polynomial $D_t(G,x)=sum_{i=gamma_t(G)}^n d_t(G,i)$, where $d_t(G,i)$ is the number of total dominating sets of $G$ of size $i$. In this paper, we study roots of the total domination polynomial of some graphs. We show that all roots of $D_t(G, x)$ lie in the circle with center $(-1, 0)$ and radius $sqrt[delta]{2^n-1}$, where $delta$ is the minimum degree of $G$. As a consequence, we prove that if $deltageq frac{2n}{3}$, then every integer root of $D_t(G, x)$ lies in the set ${-3,-2,-1,0}$." @default.
- W2997507220 created "2020-01-10" @default.
- W2997507220 creator A5029127053 @default.
- W2997507220 creator A5051558525 @default.
- W2997507220 date "2019-12-11" @default.
- W2997507220 modified "2023-10-14" @default.
- W2997507220 title "ON THE ROOTS OF TOTAL DOMINATION POLYNOMIAL OF GRAPHS, II" @default.
- W2997507220 doi "https://doi.org/10.22190/fumi1904659a" @default.
- W2997507220 hasPublicationYear "2019" @default.
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