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Bableen Kaur - One of the best experts on this subject based on the ideXlab platform.
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beck s Zero divisor graph in the realm of Signed graph
National Academy Science Letters-india, 2020Co-Authors: Deepa Sinha, Bableen KaurAbstract:For a commutative ring R with unity ($$1\ne 0$$), the Zero-divisor graph of R, denoted by $$\varGamma (R)$$, is a simple graph with vertices as elements of R and two distinct vertices are adjacent whenever the product of the vertices is Zero. Further, its Signed Zero-divisor graph is an ordered pair $$\varGamma _{\varSigma }(R):= (\varGamma (R), \sigma )$$, where for an edge xy, $$\sigma (xy)$$ is ‘$$+$$’ if either x or y or both is a nonZero Zero-divisor and ‘−’ otherwise. This article aims at gaining a deeper insight into Signed Zero-divisor graphs by investigating properties such as balancing, clusterability, sign-compatibility, consistency, $$\mathcal {C}$$-sign-compatibility, and $$\mathcal {C}$$-consistency.
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Signed Zero-Divisor Graph
Electronic Notes in Discrete Mathematics, 2017Co-Authors: Deepa Sinha, Deepakshi Sharma, Bableen KaurAbstract:Abstract Let R be a finite commutative ring with unity ( 1 ≠ 0 ) and let Z ( R ) ⁎ be the set of non-Zero Zero-divisors of R. We associate a (simple) graph Γ ( R ) to R with vertices as elements of R and for distinct x , y ∈ R , the vertices x and y are adjacent if and only if xy = 0. Further, its Signed Zero-divisor graph is an ordered pair Γ Σ ( R ) : = ( Γ ( R ) , σ ) , where for an edge ab, σ ( a b ) is ‘+’ if a ∈ Z ( R ) ⁎ or b ∈ Z ( R ) ⁎ and ‘−’ otherwise. This paper aims at gaining a deeper insight into Signed Zero-divisor graph by investigating properties like, balancing, clusterability, sign-compatibility and consistency.
Deepa Sinha - One of the best experts on this subject based on the ideXlab platform.
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beck s Zero divisor graph in the realm of Signed graph
National Academy Science Letters-india, 2020Co-Authors: Deepa Sinha, Bableen KaurAbstract:For a commutative ring R with unity ($$1\ne 0$$), the Zero-divisor graph of R, denoted by $$\varGamma (R)$$, is a simple graph with vertices as elements of R and two distinct vertices are adjacent whenever the product of the vertices is Zero. Further, its Signed Zero-divisor graph is an ordered pair $$\varGamma _{\varSigma }(R):= (\varGamma (R), \sigma )$$, where for an edge xy, $$\sigma (xy)$$ is ‘$$+$$’ if either x or y or both is a nonZero Zero-divisor and ‘−’ otherwise. This article aims at gaining a deeper insight into Signed Zero-divisor graphs by investigating properties such as balancing, clusterability, sign-compatibility, consistency, $$\mathcal {C}$$-sign-compatibility, and $$\mathcal {C}$$-consistency.
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Signed Zero-Divisor Graph
Electronic Notes in Discrete Mathematics, 2017Co-Authors: Deepa Sinha, Deepakshi Sharma, Bableen KaurAbstract:Abstract Let R be a finite commutative ring with unity ( 1 ≠ 0 ) and let Z ( R ) ⁎ be the set of non-Zero Zero-divisors of R. We associate a (simple) graph Γ ( R ) to R with vertices as elements of R and for distinct x , y ∈ R , the vertices x and y are adjacent if and only if xy = 0. Further, its Signed Zero-divisor graph is an ordered pair Γ Σ ( R ) : = ( Γ ( R ) , σ ) , where for an edge ab, σ ( a b ) is ‘+’ if a ∈ Z ( R ) ⁎ or b ∈ Z ( R ) ⁎ and ‘−’ otherwise. This paper aims at gaining a deeper insight into Signed Zero-divisor graph by investigating properties like, balancing, clusterability, sign-compatibility and consistency.
Deepakshi Sharma - One of the best experts on this subject based on the ideXlab platform.
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Signed Zero-Divisor Graph
Electronic Notes in Discrete Mathematics, 2017Co-Authors: Deepa Sinha, Deepakshi Sharma, Bableen KaurAbstract:Abstract Let R be a finite commutative ring with unity ( 1 ≠ 0 ) and let Z ( R ) ⁎ be the set of non-Zero Zero-divisors of R. We associate a (simple) graph Γ ( R ) to R with vertices as elements of R and for distinct x , y ∈ R , the vertices x and y are adjacent if and only if xy = 0. Further, its Signed Zero-divisor graph is an ordered pair Γ Σ ( R ) : = ( Γ ( R ) , σ ) , where for an edge ab, σ ( a b ) is ‘+’ if a ∈ Z ( R ) ⁎ or b ∈ Z ( R ) ⁎ and ‘−’ otherwise. This paper aims at gaining a deeper insight into Signed Zero-divisor graph by investigating properties like, balancing, clusterability, sign-compatibility and consistency.
Mehran Mesbahi - One of the best experts on this subject based on the ideXlab platform.
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Strong Structural Controllability of Signed Networks.
arXiv: Optimization and Control, 2019Co-Authors: Shima Sadat Mousavi, Mohammad Haeri, Mehran MesbahiAbstract:In this paper, we discuss the controllability of a family of linear time-invariant (LTI) networks defined on a Signed graph. In this direction, we introduce the notion of positive and negative Signed Zero forcing sets for the controllability analysis of positive and negative eigenvalues of system matrices with the same sign pattern. A sufficient combinatorial condition that ensures the strong structural controllability of Signed networks is then proposed. Moreover, an upper bound on the maximum multiplicity of positive and negative eigenvalues associated with a Signed graph is provided.
Shima Sadat Mousavi - One of the best experts on this subject based on the ideXlab platform.
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Strong Structural Controllability of Signed Networks.
arXiv: Optimization and Control, 2019Co-Authors: Shima Sadat Mousavi, Mohammad Haeri, Mehran MesbahiAbstract:In this paper, we discuss the controllability of a family of linear time-invariant (LTI) networks defined on a Signed graph. In this direction, we introduce the notion of positive and negative Signed Zero forcing sets for the controllability analysis of positive and negative eigenvalues of system matrices with the same sign pattern. A sufficient combinatorial condition that ensures the strong structural controllability of Signed networks is then proposed. Moreover, an upper bound on the maximum multiplicity of positive and negative eigenvalues associated with a Signed graph is provided.