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Uniform Number of a Graph

Publication Type : Journal Article

Publisher : Iranian Journal of Mathematical Sciences and Informatics

Source : Iranian Journal of Mathematical Sciences and Informatics, Volume 15, Issue 2, p.77-99 (2020)

Url : http://ijmsi.ir/article-1-1144-en.html

Keywords : detour distance, graphs, Hamiltonian connected graphs., uniform number

Campus : Coimbatore

School : School of Engineering

Department : Mathematics

Year : 2020

Abstract : 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 $f_M: M^crightarrow mathcalP(X) - emptyset$ 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 $mathcalP(X)$ 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.

Cite this Research Publication : K. Abhishek and E. Mohankumar, “Uniform Number of a Graph”, Iranian Journal of Mathematical Sciences and Informatics, vol. 15, no. 2, pp. 77-99, 2020.

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