Master’s Thesis – Pure Mathematics / Department of Mathematics

College of Computer Science and Mathematics

For the student: Nabaa Ahmed Jar-Allah Ahmed Al-Jawadi

The Master’s thesis, titled

“Graphing polynomial with fractional exponents for some special graphs ”

was defended in the discussion hall of the College of Computer Science and Mathematics at the University of Mosul on Sunday, September, 6, 2026.

Student: Nabaa Ahmed Jar-Allah Ahmed Al-Jawadi

Supervised by: Asst.Dr.  Raghad Abdulaziz Mustafa

Abstract

This thesis investigates a fractional distance defined in terms of the ordinary distance between vertices of a nontrivial simple connected graph. Based on this distance, a graph polynomial with fractional exponents is introduced, whose coefficients count the unordered pairs of distinct vertices at each fractional distance. The corresponding Wiener index and average distance are also derived. Explicit expressions for the polynomial and these two distance-based measures are obtained for selected families of graphs. The study further examines these quantities for graphs obtained by joining a collection of vertex-disjoint graphs and by applying the Mycielski construction.

The discussion committee consists of

• Prof. Dr. Nizar Hamdoon Shuker (Chairman)
• Prof. Dr. Raida Dawood Mahmoud (Member)
• Prof. Dr.  Ahmed Mohammed Ali (Member)