In this paper, we introduce the concept of co-common neighborhood domination number (CCN-dominati... more In this paper, we introduce the concept of co-common neighborhood domination number (CCN-domination number) γccn(G) of a graph G and we study its relation with the standard domination number γ(G). We also define CCN-independence number βccn(G), total CCNdomination number γtccn(G), CCN-covering number αccn(G) and CCN-domatic number.
Let R be a 2-torsion free prime ring with center Z, right Utumi quotient ring U , generalized der... more Let R be a 2-torsion free prime ring with center Z, right Utumi quotient ring U , generalized derivation F associated with a nonzero derivation d of R and L a Lie ideal of R. If F (uv) n = F (u) m F (v) l or F (uv) n = F (v) l F (u) m for all u, v ∈ L, where m, n, l are fixed positive integers, then L ⊆ Z. We also examine the case where R is Ahmad N. Alkenani et al. a semiprime ring. Finally, as an application we obtain some range inclusion results of continuous or spectrally bounded generalized derivations on non-commutative Banach algebras.
In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ... more In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy () E G NCN , NCN-energy for some standard graphs is obtained and an upper bound for () E G NCN is found when G is a strongly regular graph. Also the relation between common neighbourhood energy and non-common neighbourhood energy of a graph is established.
By the degree, equitable adjacency between vertices can be redefine almost all of the variants of... more By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equitable regularity, equitable connected graph and equitable complete graph. Some new families of graphs and some interesting results are obtained.
We present two new constructions of entanglement-assisted quantum error-correcting codes using so... more We present two new constructions of entanglement-assisted quantum error-correcting codes using some fundamental properties of (classical) linear codes in an effective way. The main ideas include linear complementary dual codes and related concatenation constructions. Numerical examples in modest lengths show that our constructions perform better than known constructions in the literature. We also give a proof on a generalization of binary Singleton type bound on entanglement-assisted quantum error-correcting codes to arbitrary q-ary entanglement-assisted quantum error-correcting codes.
In this paper, we introduce the concept of co-common neighborhood domination number (CCN-dominati... more In this paper, we introduce the concept of co-common neighborhood domination number (CCN-domination number) γccn(G) of a graph G and we study its relation with the standard domination number γ(G). We also define CCN-independence number βccn(G), total CCN-domination number γ tccn (G), CCN-covering number αccn(G) and CCN-domatic number.
In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ... more In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy E_{NCN}(G). NCN-energy for some standard graphs is obtained and an upper bound for E_{NCN}(G) is found when G is a strongly regular graph. Also the relation between common neighbourhood energy and non-common neighbourhood energy of a graph is established.
Let be a graph. If , G V E is a function from the vertex set V G to the set of positi... more Let be a graph. If , G V E is a function from the vertex set V G to the set of positive integers. Then two vertices are
It is known that every class-regular symmetric μ, m -net is tactical. Also it is known that all μ... more It is known that every class-regular symmetric μ, m -net is tactical. Also it is known that all μ, mnets with m 2 or μ 1 are tactical. In the work of Al-Kenani and Mavron 2003 , it is proved that every symmetric net with m 3 is tactical if and only if it is class regular. In this paper, we construct 2, 4 -net and show that it is class regular and therefore tactical. New necessary and sufficient conditions are given for a symmetric net to admit a nonidentity bitranslation.
Journal of The London Mathematical Society-second Series, 2003
... m × µ2m, such that the columns of each Ki correspond to permutations of {1, 2,...,m} in these... more ... m × µ2m, such that the columns of each Ki correspond to permutations of {1, 2,...,m} in thesequence representation of ... not class-regular and exactly two non-isomorphic class-regular (3,3)-nets and hence exactly two inequivalent 9 × 9 generalised Hadamard matrices over the ...
It is known that the designs PG n−1 (n, q) in some cases have spreads of maximal -arcs. Here a -a... more It is known that the designs PG n−1 (n, q) in some cases have spreads of maximal -arcs. Here a -arc is a non-empty subset of points that meets every hyperplane in 0 or points. The situation for designs in general is not so well known. This paper establishes an equivalence between the existence of a spread of -arcs in the complement of a Hadamard design and the existence of an affine design and a symmetric design which is also the complement of a Hadamard design.
In this paper, we introduce the concept of co-common neighborhood domination number (CCN-dominati... more In this paper, we introduce the concept of co-common neighborhood domination number (CCN-domination number) γccn(G) of a graph G and we study its relation with the standard domination number γ(G). We also define CCN-independence number βccn(G), total CCNdomination number γtccn(G), CCN-covering number αccn(G) and CCN-domatic number.
Let R be a 2-torsion free prime ring with center Z, right Utumi quotient ring U , generalized der... more Let R be a 2-torsion free prime ring with center Z, right Utumi quotient ring U , generalized derivation F associated with a nonzero derivation d of R and L a Lie ideal of R. If F (uv) n = F (u) m F (v) l or F (uv) n = F (v) l F (u) m for all u, v ∈ L, where m, n, l are fixed positive integers, then L ⊆ Z. We also examine the case where R is Ahmad N. Alkenani et al. a semiprime ring. Finally, as an application we obtain some range inclusion results of continuous or spectrally bounded generalized derivations on non-commutative Banach algebras.
In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ... more In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy () E G NCN , NCN-energy for some standard graphs is obtained and an upper bound for () E G NCN is found when G is a strongly regular graph. Also the relation between common neighbourhood energy and non-common neighbourhood energy of a graph is established.
By the degree, equitable adjacency between vertices can be redefine almost all of the variants of... more By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equitable regularity, equitable connected graph and equitable complete graph. Some new families of graphs and some interesting results are obtained.
We present two new constructions of entanglement-assisted quantum error-correcting codes using so... more We present two new constructions of entanglement-assisted quantum error-correcting codes using some fundamental properties of (classical) linear codes in an effective way. The main ideas include linear complementary dual codes and related concatenation constructions. Numerical examples in modest lengths show that our constructions perform better than known constructions in the literature. We also give a proof on a generalization of binary Singleton type bound on entanglement-assisted quantum error-correcting codes to arbitrary q-ary entanglement-assisted quantum error-correcting codes.
In this paper, we introduce the concept of co-common neighborhood domination number (CCN-dominati... more In this paper, we introduce the concept of co-common neighborhood domination number (CCN-domination number) γccn(G) of a graph G and we study its relation with the standard domination number γ(G). We also define CCN-independence number βccn(G), total CCN-domination number γ tccn (G), CCN-covering number αccn(G) and CCN-domatic number.
In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ... more In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy E_{NCN}(G). NCN-energy for some standard graphs is obtained and an upper bound for E_{NCN}(G) is found when G is a strongly regular graph. Also the relation between common neighbourhood energy and non-common neighbourhood energy of a graph is established.
Let be a graph. If , G V E is a function from the vertex set V G to the set of positi... more Let be a graph. If , G V E is a function from the vertex set V G to the set of positive integers. Then two vertices are
It is known that every class-regular symmetric μ, m -net is tactical. Also it is known that all μ... more It is known that every class-regular symmetric μ, m -net is tactical. Also it is known that all μ, mnets with m 2 or μ 1 are tactical. In the work of Al-Kenani and Mavron 2003 , it is proved that every symmetric net with m 3 is tactical if and only if it is class regular. In this paper, we construct 2, 4 -net and show that it is class regular and therefore tactical. New necessary and sufficient conditions are given for a symmetric net to admit a nonidentity bitranslation.
Journal of The London Mathematical Society-second Series, 2003
... m × µ2m, such that the columns of each Ki correspond to permutations of {1, 2,...,m} in these... more ... m × µ2m, such that the columns of each Ki correspond to permutations of {1, 2,...,m} in thesequence representation of ... not class-regular and exactly two non-isomorphic class-regular (3,3)-nets and hence exactly two inequivalent 9 × 9 generalised Hadamard matrices over the ...
It is known that the designs PG n−1 (n, q) in some cases have spreads of maximal -arcs. Here a -a... more It is known that the designs PG n−1 (n, q) in some cases have spreads of maximal -arcs. Here a -arc is a non-empty subset of points that meets every hyperplane in 0 or points. The situation for designs in general is not so well known. This paper establishes an equivalence between the existence of a spread of -arcs in the complement of a Hadamard design and the existence of an affine design and a symmetric design which is also the complement of a Hadamard design.
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Papers by A Alkenani