Document Type : Research Paper

Authors

• Elham Mokhtarian Dehkordi ¹
• Madjid Eshaghi ²
• Sirous Moradi ³
• Zahra Yarahmadi ⁴

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

Abstract

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.

Keywords

• directed Euler tour
• directed Euler path
• cycle
• directed graph
• connected directed graph
• directed power graph
• Eulerian power graph