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Let R be a commutative ring with unity $$1 \ne 0$$ . $${\Gamma (R)}$$ denotes the co-maximal graph of R, is a simple graph with vertex set R and $$y_1R+y_2R=R$$ if and only if two distinct vertices $$y_1$$ and $$y_2$$ are adjacent. In this article, we describe the Randić spectrum of the graphs $${\Gamma (\mathbb Z_n)}$$ in terms of proper divisors of n and we find the Randić spectrum of the co-maximal graph of $$\mathbb Z_n$$ for $$n=p^\nu ,p_1p_2$$ and $$p_1^2p_2$$ , where $$p, p_1$$ and $$p_2$$ are primes $$(p_1

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A Study of Randić Spectrum of the Co-maximal Graph

  • 会议论文

  • 发表日期：

    2025年

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  • A. Fosner,
  • M. Rashid,
  • G. Mohammad,
  • M. R. Mozumder

摘要

Let R be a commutative ring with unity $$1 \ne 0$$ . $${\Gamma (R)}$$ denotes the co-maximal graph of R, is a simple graph with vertex set R and $$y_1R+y_2R=R$$ if and only if two distinct vertices $$y_1$$ and $$y_2$$ are adjacent. In this article, we describe the Randić spectrum of the graphs $${\Gamma (\mathbb Z_n)}$$ in terms of proper divisors of n and we find the Randić spectrum of the co-maximal graph of $$\mathbb Z_n$$ for $$n=p^\nu ,p_1p_2$$ and $$p_1^2p_2$$ , where $$p, p_1$$ and $$p_2$$ are primes $$(p_1