TY - JOUR
JF - IJMSI
JO - IJMSI
VL - 15
IS - 2
PY - 2020
Y1 - 2020/10/01
TI - Uniform Number of a Graph
TT -
N2 - We introduce the notion of uniform number of a graph. The uniform number of a connected graph $G$ is the least cardinality of a nonempty subset $M$ of the vertex set of $G$ for which the function $f_M: M^crightarrow mathcal{P}(X) - {emptyset}$ defined as $f_M(x) = {D(x, y): y in M}$ is a constant function, where $D(x, y)$ is the detour distance between $x$ and $y$ in $G$ and $mathcal{P}(X)$ is power set of $X = {D(x_i, x_j): x_i neq x_j}.$ We obtain some basic results and compute the newly introduced graph parameter for some specific graphs.
SP - 77
EP - 99
AU - Kumar, A.
AU - Mohankumar, E.
AD - Amrita Vishwa Vidyapeetham, Amrita University, India.
KW - Graphs
KW - detour distance
KW - uniform number
KW - Hamiltonian connected graphs.
UR - http://ijmsi.ir/article-1-1144-en.html
ER -