Sep 2026· Journal of the Indonesian Mathematical Society· 0 citations· 16 references
Abstract
Power graphs of groups and semigroups constitute a significant class of graphs in algebraic graph theory, bridging algebraic structures and graph theoretic concepts. Further, labeling of graphs, particularly those endowed with an algebraic structure as their vertex set, is a vibrant area of research. This article contributes to this burgeoning field by exploring new classes of finite groups whose power graphs admit or forbid an important type of labeling called graceful labeling.
In this article, we prove the Defect Conjecture for Cayley graphs of abelian groups, dihedral groups, and groups of the form $\mathbb{Z}/p\mathbb{Z} \rtimes \mathbb{Z}/(p-1)\mathbb{Z}$ where $p\geq 3$ is a prime. We also compute the Iwasawa invariants of the Bowen--Franks groups associated with these graphs in several...
Debanjana Kundu, Katharina Müller, A. Newton et al.· 0 citations
We construct a family of finite local rings whose annihilating-ideal graphs are naturally described by orthogonality of subspaces of $\mathbb{F}_2^n$. For $n=4$ we determine the clique and chromatic numbers exactly and obtain \[ \omega(\AG(R_4))=5<6=\chi(\AG(R_4)). \] Thus $\AG(R_4)$ is not weakly perfect, and the Behb...
We give an alternative graph-theoretic proof that 20 is the least degree not divisible by 3 of an algebraic number having three distinct conjugates with zero sum. The proof excludes degree 16 through local constraints on vertex-transitive graphs of valency 6. The underlying graph construction can be studied in arbitrar...
Žygimantas Baronėnas, Paulius Drungilas, Jonas Jankauskas· Mathematics· 0 citations
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