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ON STRUCTURAL AND ALGEBRAIC PROPERTIES OF EDGE GEODETIC CLOSURE POLYNOMIALS IN GRAPHS.

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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]
Copyright of Advances & Applications in Discrete Mathematics is the property of Pushpa Publishing House and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: ON STRUCTURAL AND ALGEBRAIC PROPERTIES OF EDGE GEODETIC CLOSURE POLYNOMIALS IN GRAPHS.
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  Data: <searchLink fieldCode="AR" term="%22Artes+Jr%2E%2C+Rosalio+G%2E%22">Artes Jr., Rosalio G.</searchLink><relatesTo>1</relatesTo><i> rosalioartes@msutawi-tawi.edu.ph</i><br /><searchLink fieldCode="AR" term="%22Bara%2C+Zuraida+J%2E%22">Bara, Zuraida J.</searchLink><relatesTo>2</relatesTo><i> zuraidabara0268@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Hashim%2C+Adznar+S%2E%22">Hashim, Adznar S.</searchLink><relatesTo>3</relatesTo><i> adznar.hashim@sulustatecollege.edu.ph</i><br /><searchLink fieldCode="AR" term="%22Moh%2E+Jiripa%2C+Hashirin+H%2E%22">Moh. Jiripa, Hashirin H.</searchLink><relatesTo>1</relatesTo><i> hashirinmoh.jiripa@msutawi-tawi.edu.ph</i><br /><searchLink fieldCode="AR" term="%22Moh%2E+Jiripa%2C+Rashidin+H%2E%22">Moh. Jiripa, Rashidin H.</searchLink><relatesTo>1</relatesTo><i> rashidinmoh.jiripa@msutawi-tawi.edu.ph</i>
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  Data: <searchLink fieldCode="JN" term="%22Advances+%26+Applications+in+Discrete+Mathematics%22">Advances & Applications in Discrete Mathematics</searchLink>. Jul2026, Vol. 43 Issue 5, p578-585. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Star+graphs+%28Graph+theory%29%22">Star graphs (Graph theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink><br /><searchLink fieldCode="DE" term="%22Paths+%26+cycles+in+graph+theory%22">Paths & cycles in graph theory</searchLink>
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  Data: 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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  Data: <i>Copyright of Advances & Applications in Discrete Mathematics is the property of Pushpa Publishing House and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        PageCount: 11
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      – SubjectFull: Graph theory
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      – SubjectFull: Star graphs (Graph theory)
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      – SubjectFull: Combinatorics
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      – TitleFull: ON STRUCTURAL AND ALGEBRAIC PROPERTIES OF EDGE GEODETIC CLOSURE POLYNOMIALS IN GRAPHS.
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              Text: Jul2026
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              Y: 2026
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