TY - JOUR
ID - 14108
TI - The upper domatic number of powers of graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Samuel, Libin Chacko
AU - Joseph, Mayamma
AD - CHRIST (Deemed to be University), Bangalore
AD - CHRIST(Deemed to be University), Bangalore
Y1 - 2021
PY - 2021
VL - 6
IS - 1
SP - 53
EP - 65
KW - Domatic number
KW - $k$-domatic number
KW - Upper domatic partition
KW - Upper domatic number
KW - $k$-upper domatic number
DO - 10.22049/cco.2020.26913.1163
N2 - Let $A$ and $B$ be two disjoint subsets of the vertex set $V$ of a graph $G$. The set $A$ is said to dominate $B$, denoted by $A rightarrow B$, if for every vertex $u in B$ there exists a vertex $v in A$ such that $uv in E(G)$. For any graph $G$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_p}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i rightarrow V_j$ or $V_j rightarrow V_i$ or both for every $V_i, V_j in pi$, whenever $i neq j$. The textit{upper domatic number} $D(G)$ is the maximum order of an upper domatic partition. In this paper, we study the upper domatic number of powers of graphs and examine the special case when power is $2$. We also show that the upper domatic number of $k^{mathrm{th}}$ power of a graph can be viewed as its $ k$-upper domatic number.
UR - http://comb-opt.azaruniv.ac.ir/article_14108.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14108_7058eb1b6f8a087a8b1ec3b80f28c2ac.pdf
ER -