Let R be a commutative ring with unity,M be a unitary R-module and F be a simple connected graph.We examine different equivalence relations on subsets A_(f)(M)\{0},A_(s)(M)\{0}and A_(t)(M)/{0}of M,where A_(f)(M)is the...Let R be a commutative ring with unity,M be a unitary R-module and F be a simple connected graph.We examine different equivalence relations on subsets A_(f)(M)\{0},A_(s)(M)\{0}and A_(t)(M)/{0}of M,where A_(f)(M)is the set of full-annihilators,A_(s)(M)is the set of semi-annihilators and A_(t)(M)is the set of star-annihilators in M.We prove that elements x,y∈M are neighborhood similar in the annihilating graph ann_(f)(Г(M))if and only if the submodules ann(x)M and ann(y)M of M are equal.We study the isomorphism of annihilating graphs arising from M and the tensor product M⊗_(R)T^(-1)R,where T=R/C(M),C(M)={r∈R|rm=O for some O≠m∈M}.展开更多
For a finite group G,the power graph P(G)is a simple connected graph whose vertex set is the set of elements of G and two distinct vertices x and y are adjacent if and only if x^(i)=y or y^(i)=x,for 2≤i,j≤n.In this ...For a finite group G,the power graph P(G)is a simple connected graph whose vertex set is the set of elements of G and two distinct vertices x and y are adjacent if and only if x^(i)=y or y^(i)=x,for 2≤i,j≤n.In this paper,we obtain the distance Laplacian spectrum of power graphs of finite groups such as cyclic groups,dihedral groups,dicyclic groups,abelian groups and elementary abelian p groups.Moreover,we find the largest and second smallest distance Laplacian eigenvalue of power graphs of such groups.展开更多
文摘Let R be a commutative ring with unity,M be a unitary R-module and F be a simple connected graph.We examine different equivalence relations on subsets A_(f)(M)\{0},A_(s)(M)\{0}and A_(t)(M)/{0}of M,where A_(f)(M)is the set of full-annihilators,A_(s)(M)is the set of semi-annihilators and A_(t)(M)is the set of star-annihilators in M.We prove that elements x,y∈M are neighborhood similar in the annihilating graph ann_(f)(Г(M))if and only if the submodules ann(x)M and ann(y)M of M are equal.We study the isomorphism of annihilating graphs arising from M and the tensor product M⊗_(R)T^(-1)R,where T=R/C(M),C(M)={r∈R|rm=O for some O≠m∈M}.
基金Supported by SERB-DST,New Delhi,under the research project number MTR/2017/000084the third author is supported by NSFC (Grant Nos.11931006 and 11971011)。
文摘For a finite group G,the power graph P(G)is a simple connected graph whose vertex set is the set of elements of G and two distinct vertices x and y are adjacent if and only if x^(i)=y or y^(i)=x,for 2≤i,j≤n.In this paper,we obtain the distance Laplacian spectrum of power graphs of finite groups such as cyclic groups,dihedral groups,dicyclic groups,abelian groups and elementary abelian p groups.Moreover,we find the largest and second smallest distance Laplacian eigenvalue of power graphs of such groups.
