IJPAM: Volume 120, No. 1 (2018)

Title

UNIFORM NUMBERS OF CYCLIC GRAPHS

Authors

M. Elakkiya$^1$, Kumar Abhishek$^2$
$^{1,2}$Amrita School of Engineering Coimbatore
Amrita Vishwa Vidyapeetham, INDIA

Abstract

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 $f_M: M^c\rightarrow \mathcal{P}(X) - \{\emptyset\}$ 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 $X = \{D(x_i, x_j): x_i \neq x_j\}.$ In this note, we determine the uniform number for the classes of graphs having at least one cycle as its induced subgraph.

History

Received: September 5, 2017
Revised: January 11, 2018
Published: August 13, 2018

AMS Classification, Key Words

AMS Subject Classification: 05C22
Key Words and Phrases: graphs, distances, detour distance, uniform number.

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Bibliography

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M. Elakkiya, Kumar Abhishek, Uniform number of a graph, Submitted 2017.

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How to Cite?

DOI: 10.12732/ijpam.v120i1.6 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 1
Pages: 67 - 75


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