TY - JOUR
ID - 13993
TI - New results on upper domatic number of graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Samuel, Libin
AU - JOSEPH, MAYAMMA
AD - CHRIST (Deemed to be University)
AD - CHRIST(Deemed to be University) Hosur Road
Bangalore-560029
Y1 - 2020
PY - 2020
VL - 5
IS - 2
SP - 125
EP - 137
KW - domination
KW - Upper domatic partition
KW - Upper domatic number
KW - Transitivity
DO - 10.22049/cco.2019.26719.1136
N2 - For a graph $G = (V, E)$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_k}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i$ dominates $V_j$ or $V_j$ dominates $V_i$ 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. We study the properties of upper domatic number and propose an upper bound in terms of clique number. Further, we discuss the upper domatic number of certain graph classes including unicyclic graphs and power graphs of paths and cycles.
UR - http://comb-opt.azaruniv.ac.ir/article_13993.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13993_d2d2bdfc3ac890ae53ac04a1d2ad425e.pdf
ER -