id: 05163125
dt: j
an: 05163125
au: Muddebihal, M.H.; Usha, P.
ti: Semitotal block nonsplit domination in graphs.
so: J. Anal. Comput. 1, No. 1, 31-37 (2005).
py: 2005
pu: Serials Publications, New Delhi, Delhi, India
la: EN
cc: 
ut: domination; semitotal block graph; semitotal block nonsplit dominating
    number
ci: 
li: 
ab: 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 $γ_{sbn}(G)$. In this paper several bounds on $γ_{sbn}(G)$
    are proposed, e.g., $γ_{sbn}(G)\leq \vert V(G)\vert -δ(G)$ or
    $γ_{sbn}(G)\leq \vert V(G)\vert -χ(G)+1$, where $χ(G)$ denotes the
    chromatic number of $G$; also, a Nordhaus-Gaddum type result is
    deduced.
rv: Ioan Tomescu (Bucureşti)