Directed Power Graphs

Document Type : Research Paper


1 Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

2 Department of Mathematics, Semnan University, Iran

3 Department of Mathematics, Faculty of science, Lorestan University, 68151-4-4316, Khorramabad, Iran

4 Department of Mathematics, Faculty of science, Khorramabad Branch, Islamic Azad University, Khorramabad, I. R. Iran


In this article, first we introduce six types of power graphs related to a graph (or directed graph), with the help of set theory.
Then we show that these newly defined power graphs are pairwise distinct by a few examples. Finally, we discuss the relation between Eulerian being the base graph and these six power graph types. Moreover, we express the relation between pairwise Eulerian of these power graphs.


[1] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer Publishing Company, Incorporated, 2008.
[2] G. Chartrand and P. Zha, A First Course in Graph Theory, Dover Publication, Inc. Mineola, New York, Gary Chartrand and Ping Zhang All rights reserved, 2012.
[3] M.M. Cabigting Lunar and R. Aguilar Robles, Characterization and Structure of a Power Set Graph, College of Arts and Sciences, Batangas State University PabloBorbon Main I, Rizal Ave., Batangas City, Philippines, 2019.
[4] M.A. Shalu and S. Devi Yammini, Counting maximal independent sets in power set graphs, Indian Institute of Information Technology Design & Manufacturing (IIITD & M) Kancheepuram, India, 2014.
[5] A. Treier, Universal graph powerset, Conference Series, Sobolev Institute of Mathematics of SB RAS, Omsk, Russia, 2019.
[6] R. J. Wilson, Introduction to Graph Theory, Third Edition, Longman, 1985.
Volume 12, Issue 2
November 2021
Pages 2619-2657
  • Receive Date: 19 March 2021
  • Revise Date: 09 July 2021
  • Accept Date: 04 August 2021