Seoud, M., Mohamed Hafez, H. (2018). On Powers of Some Graph Operations. Mathematics Interdisciplinary Research, 3(1), 31-43. doi: 10.22052/mir.2018.85618.1062

Mohamed Seoud; Hamdy Mohamed Hafez. "On Powers of Some Graph Operations". Mathematics Interdisciplinary Research, 3, 1, 2018, 31-43. doi: 10.22052/mir.2018.85618.1062

Seoud, M., Mohamed Hafez, H. (2018). 'On Powers of Some Graph Operations', Mathematics Interdisciplinary Research, 3(1), pp. 31-43. doi: 10.22052/mir.2018.85618.1062

Seoud, M., Mohamed Hafez, H. On Powers of Some Graph Operations. Mathematics Interdisciplinary Research, 2018; 3(1): 31-43. doi: 10.22052/mir.2018.85618.1062

^{1}Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt

^{2}Department of Basic science, Faculty of Computers and Information, Fayoum University, Fayoum 63514, Egypt

Abstract

Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.