Subgroup Sum Graphs of Finite Abelian Groups

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