گراف پوچ‎ساز گروه‎های آبلی

نویسندگان
دانشگاه یاسوج
چکیده
در این مقاله گراف پوچ‎ساز ( گروه‎های آبلی) بررسی خواهند شد. گراف پوچ‎ساز یک گروه آبلی مانند M را با نماد G(M) نمایش می‎دهیم. در این راستا نشان خواهیم داد، گراف پوچساز M تهی است اگر و تنها اگر M≌ Z یا M یک گروه آبلی ساده باشد. علاوه بر این تمام گروه‎های آبلی متناهی- تولید شده که گراف پوچ‎ساز آن‎ها کامل، دوبخشی یا دوبخشی کامل هستند، مشخص خواهند شد. در مرجع [14] نویسندگان گراف مقسوم‎علیه صفرگروه‎های آبلی را مطرح و مورد بررسی قرار دادند. در این مقاله ما الگوریتمی بر اساس نرم‎افزار میپل ارائه خواهیم داد که گراف مقسوم‎علیه صفر و گراف پوچ‎ساز یک گروه آبلی دوری را هم زمان رسم می‎کند.
کلیدواژه‌ها

عنوان مقاله English

Annihilating Graph of Abelian Groups

نویسندگان English

saeed safaeeyan
Soraya Barzegar
University
چکیده English

In [18], the author associated a graph to an R -module M which is precisely a generalization of annihilating ideal graph of a commutative ring, see [15] and [16].

Inasmuch as Abelian groups are precisely Z-modules, in this paper we relate an annihilating graph to an Abelian group , denoted by G(M) , and study this graph. We show that G(M) is an empty graph if and only if either M≅Z or M is a simple Abelian group. Moreover, we show that G(M) is a finite graph if and only if M is a finite Abelian group. Among other things, we characterize Abelian groups for which their annihilating graphs are complete, bipartite or complete bipartite graphs.

کلیدواژه‌ها English

modules
Abelian Groups
Annihilating graph
Graph
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