A fundamental theorem on graph operators
A graph operator is a function [Formula: see text] defined on some set of graphs such that whenever two graphs G and H are isomorphic, written [Formula: see text], then [Formula: see text]. For a graph G not in the domain of [Formula: see text], we put [Formula: see text]. Also, let us define [Formu...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2025-01-01
|
| Series: | Mathematics Open |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S2811007225500105 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849235943439990784 |
|---|---|
| author | Severino V. Gervacio |
| author_facet | Severino V. Gervacio |
| author_sort | Severino V. Gervacio |
| collection | DOAJ |
| description | A graph operator is a function [Formula: see text] defined on some set of graphs such that whenever two graphs G and H are isomorphic, written [Formula: see text], then [Formula: see text]. For a graph G not in the domain of [Formula: see text], we put [Formula: see text]. Also, let us define [Formula: see text], and for any integer [Formula: see text], [Formula: see text] We prove that if [Formula: see text] is a graph operator, then the sequence [Formula: see text] has only three possible types of behavior. Either [Formula: see text] for some integer [Formula: see text], or [Formula: see text], or there exist integers [Formula: see text], [Formula: see text] such that the graphs [Formula: see text] are non-isomorphic ([Formula: see text], and [Formula: see text] for all integers [Formula: see text]. We illustrate this using two new graph operators, namely, the path graph operator and the claw graph operator. |
| format | Article |
| id | doaj-art-7a53d5c38dd44a0aac9c32947a1fbac9 |
| institution | Kabale University |
| issn | 2811-0072 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Mathematics Open |
| spelling | doaj-art-7a53d5c38dd44a0aac9c32947a1fbac92025-08-20T04:02:32ZengWorld Scientific PublishingMathematics Open2811-00722025-01-010410.1142/S2811007225500105A fundamental theorem on graph operatorsSeverino V. Gervacio0Department of Mathematics and Statistics, De La Salle University, 0922 Manila, PhilippinesA graph operator is a function [Formula: see text] defined on some set of graphs such that whenever two graphs G and H are isomorphic, written [Formula: see text], then [Formula: see text]. For a graph G not in the domain of [Formula: see text], we put [Formula: see text]. Also, let us define [Formula: see text], and for any integer [Formula: see text], [Formula: see text] We prove that if [Formula: see text] is a graph operator, then the sequence [Formula: see text] has only three possible types of behavior. Either [Formula: see text] for some integer [Formula: see text], or [Formula: see text], or there exist integers [Formula: see text], [Formula: see text] such that the graphs [Formula: see text] are non-isomorphic ([Formula: see text], and [Formula: see text] for all integers [Formula: see text]. We illustrate this using two new graph operators, namely, the path graph operator and the claw graph operator.https://www.worldscientific.com/doi/10.1142/S2811007225500105Graph operatorinduced subgraphintersection graph |
| spellingShingle | Severino V. Gervacio A fundamental theorem on graph operators Mathematics Open Graph operator induced subgraph intersection graph |
| title | A fundamental theorem on graph operators |
| title_full | A fundamental theorem on graph operators |
| title_fullStr | A fundamental theorem on graph operators |
| title_full_unstemmed | A fundamental theorem on graph operators |
| title_short | A fundamental theorem on graph operators |
| title_sort | fundamental theorem on graph operators |
| topic | Graph operator induced subgraph intersection graph |
| url | https://www.worldscientific.com/doi/10.1142/S2811007225500105 |
| work_keys_str_mv | AT severinovgervacio afundamentaltheoremongraphoperators AT severinovgervacio fundamentaltheoremongraphoperators |