The graded annihilating submodule graph

In this paper, we study the graded annihilating graph for submodules, representing graded submodules as vertices connected by edges following a specific pattern. Our exploration leads us through the intricacies of this graph, uncovering insights into their connectivity, girth, bipartition, and compl...

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Main Authors: Mamoon Ahmed, Fida Moh’d
Format: Article
Language:English
Published: Taylor & Francis Group 2025-04-01
Series:AKCE International Journal of Graphs and Combinatorics
Subjects:
Online Access:https://www.tandfonline.com/doi/10.1080/09728600.2025.2492075
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author Mamoon Ahmed
Fida Moh’d
author_facet Mamoon Ahmed
Fida Moh’d
author_sort Mamoon Ahmed
collection DOAJ
description In this paper, we study the graded annihilating graph for submodules, representing graded submodules as vertices connected by edges following a specific pattern. Our exploration leads us through the intricacies of this graph, uncovering insights into their connectivity, girth, bipartition, and completeness within graded modules, establishing connections between these graded annihilating graph submodules and their ungraded counterparts. We also extend prior work on finite girth conditions of annihilating graphs for modules. Our contributions include two comprehensive criteria for graded modules (Theorem 3.7 and Corollary 3.8), which also apply to non-graded modules with trivial gradation. These findings have implications for this article and future research.
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record_format Article
series AKCE International Journal of Graphs and Combinatorics
spelling doaj-art-45cc0426fca9460bb4a6ef0c522935b22025-08-20T02:20:12ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742025-04-011910.1080/09728600.2025.2492075The graded annihilating submodule graphMamoon Ahmed0Fida Moh’d1Department of Basic Sciences, Princess Sumaya University for Technology, Amman, JordanDepartment of Basic Sciences, Princess Sumaya University for Technology, Amman, JordanIn this paper, we study the graded annihilating graph for submodules, representing graded submodules as vertices connected by edges following a specific pattern. Our exploration leads us through the intricacies of this graph, uncovering insights into their connectivity, girth, bipartition, and completeness within graded modules, establishing connections between these graded annihilating graph submodules and their ungraded counterparts. We also extend prior work on finite girth conditions of annihilating graphs for modules. Our contributions include two comprehensive criteria for graded modules (Theorem 3.7 and Corollary 3.8), which also apply to non-graded modules with trivial gradation. These findings have implications for this article and future research.https://www.tandfonline.com/doi/10.1080/09728600.2025.2492075Graphgraded ringsgraded modulesannihilating submodule graphgraded annihilating submodule graphgirth
spellingShingle Mamoon Ahmed
Fida Moh’d
The graded annihilating submodule graph
AKCE International Journal of Graphs and Combinatorics
Graph
graded rings
graded modules
annihilating submodule graph
graded annihilating submodule graph
girth
title The graded annihilating submodule graph
title_full The graded annihilating submodule graph
title_fullStr The graded annihilating submodule graph
title_full_unstemmed The graded annihilating submodule graph
title_short The graded annihilating submodule graph
title_sort graded annihilating submodule graph
topic Graph
graded rings
graded modules
annihilating submodule graph
graded annihilating submodule graph
girth
url https://www.tandfonline.com/doi/10.1080/09728600.2025.2492075
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