A note on annihilating ideal graph of n Z

International Conference on Algebra and Discrete Mathematics on January 8 to 10, 2018 Department of Mathematics, DDE, Madurai Kamaraj University, Tamil Nadu, India International Journal of Computer Science (IJCS) Published by SK Research Group of Companies (SKRGC)

Abstract

Let be a commutative ring with identity and the set of non-zero ideals with non-zero annihilators. The annihilating-ideal graph of is defined as the graph with the vertex set and two distinct vertices and are adjacent if and only if . In this paper, we obtain a characterization for the annihilating-ideal graph to be unicyclic, claw-free and outerplanar when R ) ( * R A R ) (RAG) ( * R A 1 I 2 I (0) = 2 1 I I ) (RAG. = n R

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Keywords

claw-free graph, outer planar graph, unicyclic graph.