M_n – Polynomials of Some Special Graphs

• Raghad Mustafa University of Mosul
• Ahmed M. Ali
• AbdulSattar M. Khidhir Computer Center, Northern Technical University
Keywords: max–n–distance, M_n –Polynomial, M_n –index

Abstract

Let  be a connected graph with vertices set  and edges set . The ordinary distance between any two vertices of  is a mapping  from  into a nonnegative integer number such that  is the length of a shortest  path. The maximum distance between two subsets  and  of   is the maximum distance between any two vertices  and  such that  belong to  and  belong to . In this paper, we take a special case of maximum distance when  consists of one vertex and  consists of  vertices, . This distance is defined by: where  is the order of  a graph .

In this paper, we defined  – polynomials based on the maximum distance between a vertex  in  and a subset  that has vertices of a vertex set of  and  – index. Also, we find  polynomials for some special graphs, such as: complete, complete bipartite, star, wheel, and fan graphs, in addition to  polynomials of path, cycle, and Jahangir graphs. Then we determine the indices of these distances.

Published
2021-07-01
How to Cite
Mustafa, R., Ali, A. M., & Khidhir, A. M. (2021). M_n – Polynomials of Some Special Graphs. Iraqi Journal of Science, 62(6), 1986-1993. https://doi.org/10.24996/ijs.2021.62.6.24
Issue
Section
Mathematics  