Bibliographic Details
| Title: |
ON STRUCTURAL AND ALGEBRAIC PROPERTIES OF EDGE GEODETIC CLOSURE POLYNOMIALS IN GRAPHS. |
| Authors: |
Artes Jr., Rosalio G.1 rosalioartes@msutawi-tawi.edu.ph, Bara, Zuraida J.2 zuraidabara0268@gmail.com, Hashim, Adznar S.3 adznar.hashim@sulustatecollege.edu.ph, Moh. Jiripa, Hashirin H.1 hashirinmoh.jiripa@msutawi-tawi.edu.ph, Moh. Jiripa, Rashidin H.1 rashidinmoh.jiripa@msutawi-tawi.edu.ph |
| Source: |
Advances & Applications in Discrete Mathematics. Jul2026, Vol. 43 Issue 5, p578-585. 11p. |
| Subjects: |
Polynomials, Graph theory, Star graphs (Graph theory), Combinatorics, Paths & cycles in graph theory |
| Abstract: |
The edge geodetic closure polynomial is a recently introduced graph polynomial that enumerates 2-closure edge geodetic sets according to their cardinalities. In this paper, further structural properties of this polynomial are established. General coefficient properties are first derived, including its first coefficient, degree bound, and total-set interpretation. Explicit formulas are then obtained for cycles and star graphs, while a recurrence relation and a closed form are presented for path graphs. These results extend the initial study on complete graphs, paths, and complete bipartite graphs, and provide additional insight into the combinatorial behavior of edge geodetic closure sets. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
