Edge Degree Weight of Sequential Join of Graphs

  • Khidir R. Sharaf University of Zakho
  • Didar A. Ali University of Zakho
Keywords: Graph Theory, Edge degree weights

Abstract

Let the weight w of an edge e= uv={u,v} of a graph G be defined by w(e)=deg(u)+deg(v)-2 and the weight of G be defined by w(G)= ∑ e ∈ E(G)w(e), where E(G) is the edge set of G. In this paper the weights of joins, sequential joins, unions, intersections, and products (Cartesian and Tensor) of sets of graphs are obtained. This leads to a variety of open questions and new studies.

Author Biographies

Khidir R. Sharaf, University of Zakho

Dept. of Mathematics, Faculty of Science University of Zakho, Kurdistan Region-Iraq.

Didar A. Ali, University of Zakho

Dept. of Mathematics, Faculty of Science University of Zakho, Kurdistan Region-Iraq.

References

L.W. Beineke, and R.J. Wilson; (1978), Selected Topics in Graph Theory, Academic Press, Inc., London.
F. Buckley and F. Harary; (1990), Distance in Graphs, Addison–Wesley, New York.
E.G. DuCasse, M.L. Gargano, M.B. Kattimani, and L.V. Quintas; (2009), The edge degree weight sum of a graph, Graph Theory Notes of New York,LVI:6, 38–43.
E.G.DuCasse and L.V.Quintas;(2011), Edge degree weight generalizations. Graph Theory Notes of New York, LXI:4, 25–30.
M.B. Kattimani; (2008), A note on edge degree weighted sums of a graph, Graph Theory Notes of New York, LV:3,25–26.
Published
2013-09-30
How to Cite
Sharaf, K., & Ali, D. (2013). Edge Degree Weight of Sequential Join of Graphs. Science Journal of University of Zakho, 1(2), 854-861. Retrieved from https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/431
Section
Science Journal of University of Zakho