The Sombor index for a graph G with vertex set V and edge set E is defined as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\sum _{vw\in E}\sqrt{d_v^2+d_w^2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mo>∑</mo> <mrow> <mi>v</mi> <mi>w</mi> <mo>∈</mo> <mi>E</mi> </mrow> </msub> <msqrt> <mrow> <msubsup> <mi>d</mi> <mi>v</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>d</mi> <mi>w</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$d_v$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mi>v</mi> </msub> </math></EquationSource> </InlineEquation> denotes the number of edges incident on the vertex <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$v\in V$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>v</mi> <mo>∈</mo> <mi>V</mi> </mrow> </math></EquationSource> </InlineEquation>. The annihilating-ideal graph of a commutative ring R consists the set of non-trivial ideals with non-zero annihilator as the vertex set and two distinct vertices are joined by an edge if their product is zero. In this paper, the Sombor index of annihilating-ideal graphs associated with <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathbb {Z}_n$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>, the ring of integers modulo n, is discussed.

Computing the Sombor index in annihilating-ideal graphs

期刊论文
发表日期：

2026年4月6日

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M. J. Nikmehr,
R. Nikandish,
M. Mehrara

摘要

The Sombor index for a graph G with vertex set V and edge set E is defined as $\sum _{vw\in E}\sqrt{d_v^2+d_w^2}$ $\sum_{v w \in E} \sqrt{d_{v}^{2} + d_{w}^{2}}$ , where $d_v$ $d_{v}$ denotes the number of edges incident on the vertex $v\in V$ $v \in V$ . The annihilating-ideal graph of a commutative ring R consists the set of non-trivial ideals with non-zero annihilator as the vertex set and two distinct vertices are joined by an edge if their product is zero. In this paper, the Sombor index of annihilating-ideal graphs associated with $\mathbb {Z}_n$ $Z_{n}$ , the ring of integers modulo n, is discussed.