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Kumar A, Mohankumar E. Uniform Number of a Graph. IJMSI 2020; 15 (2) :77-99
URL: http://ijmsi.ir/article-1-1144-en.html
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.
Type of Study: Research paper | Subject: General

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