@article {IOPORT.05163125,
    author       = {Muddebihal, M.H. and Usha, P.},
    title        = {Semitotal block nonsplit domination in graphs.},
    year         = {2005},
    journal      = {Journal of Analysis and Computation},
    volume       = {1},
    number       = {1},
    issn         = {0973-2861, 0972-2861},
    pages        = {31-37},
    publisher    = {Serials Publications, New Delhi, Delhi, India},
    abstract     = {For a graph $G$ the semitotal block graph of $G$, denoted by $H(G)$, is defined as the graph whose vertex set is the union of the vertex and block sets of $G$, in which two vertices are adjacent if and only if corresponding vertices of $G$ are adjacent or corresponding members are incident. A dominating set $D$ of $H(G)$ such that the induced subgraph $\langle V(H(G))-D\rangle$ is connected is called a semitotal block nonsplit (SBN) dominating set and the minimum cardinality of a SBN dominating set of $G$ is called the SBN domination number of $G$ and is denoted by $\gamma _{sbn}(G)$. In this paper several bounds on $\gamma _{sbn}(G)$ are proposed, e.g., $\gamma _{sbn}(G)\leq \vert V(G)\vert -\delta (G)$ or $\gamma _{sbn}(G)\leq \vert V(G)\vert -\chi (G)+1$, where $\chi (G)$ denotes the chromatic number of $G$; also, a Nordhaus-Gaddum type result is deduced.},
    reviewer     = {Ioan Tomescu (Bucure\c{s}ti)},
    identifier   = {05163125},
}