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Directed Power Graphs | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 2619-2657 اصل مقاله (507.03 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5443 | ||
| نویسندگان | ||
| Elham Mokhtarian Dehkordi1؛ Madjid Eshaghi* 2؛ Sirous Moradi3؛ Zahra Yarahmadi4 | ||
| 1Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran | ||
| 2Department of Mathematics, Semnan University, Iran | ||
| 3Department of Mathematics, Faculty of science, Lorestan University, 68151-4-4316, Khorramabad, Iran | ||
| 4Department of Mathematics, Faculty of science, Khorramabad Branch, Islamic Azad University, Khorramabad, I. R. Iran | ||
| تاریخ دریافت: 29 اسفند 1399، تاریخ بازنگری: 18 تیر 1400، تاریخ پذیرش: 13 مرداد 1400 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| directed Euler tour؛ directed Euler path؛ cycle؛ directed graph؛ connected directed graph؛ directed power graph؛ Eulerian power graph | ||
| مراجع | ||
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[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. | ||
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