%0 Journal Article
%A Kumar, A.
%A Mohankumar, E.
%T Uniform Number of a Graph
%J Iranian Journal of Mathematical Sciences and Informatics
%V 15
%N 2
%U http://ijmsi.ir/article-1-1144-en.html
%R
%D 2020
%K Graphs, detour distance, uniform number, Hamiltonian connected graphs.,
%X 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.
%> http://ijmsi.ir/article-1-1144-en.pdf
%P 77-99
%& 77
%!
%9 Research paper
%L A-10-2882-1
%+ Amrita Vishwa Vidyapeetham, Amrita University, India.
%G eng
%@ 1735-4463
%[ 2020