TY - JOUR T1 - Uniform Number of a Graph TT - JF - IJMSI JO - IJMSI VL - 15 IS - 2 UR - http://ijmsi.ir/article-1-1144-en.html Y1 - 2020 SP - 77 EP - 99 KW - Graphs KW - detour distance KW - uniform number KW - Hamiltonian connected graphs. 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. M3 ER -