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


 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.

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