Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
149 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Subgroup sum graphs of finite abelian groups (2111.05748v1)

Published 10 Nov 2021 in math.CO

Abstract: Let $G$ be a finite abelian group, written additively, and $H$ a subgroup of~$G$. The \emph{subgroup sum graph} $\Gamma_{G,H}$ is the graph with vertex set $G$, in which two distinct vertices $x$ and $y$ are joined if $x+y\in H\setminus{0}$. These graphs form a fairly large class of Cayley sum graphs. Among cases which have been considered previously are the \emph{prime sum graphs}, in the case where $H=pG$ for some prime number $p$. In this paper we present their structure and a detailed analysis of their properties. We also consider the simpler graph $\Gamma+_{G,H}$, which we refer to as the \emph{extended subgroup sum graph}, in which $x$ and $y$ are joined if $x+y\in H$: the subgroup sum is obtained by removing from this graph the partial matching of edges having the form ${x,-x}$ when $2x\ne0$. We study perfectness, clique number and independence number, connectedness, diameter, spectrum, and domination number of these graphs and their complements. We interpret our general results in detail in the prime sum graphs.

Summary

We haven't generated a summary for this paper yet.