Let?G=(V,E)? be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two vertices?u, v ∈ V(G)? are?φ -equitable if|φ(u)-φ(v)|≤1.By the degree, equitable adjacency between ve...Let?G=(V,E)? be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two vertices?u, v ∈ V(G)? are?φ -equitable if|φ(u)-φ(v)|≤1.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.展开更多
In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ,?,?NCN-energy for some standard graphs is obtained and an upper bound for ?is found when G is a strongly regular graph....In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ,?,?NCN-energy for some standard graphs is obtained and an upper bound for ?is found when G is a strongly regular graph. Also the relation between common neigh-bourhood energy and non-common neighbourhood energy of a graph is established.展开更多
Let G= (V, E) be a graph and A(G) is the collection of all minimal equitable dominating set of G. The middle equitable dominating graph of G is the graph denoted by Med(G) with vertex set the disjoint union of V∪A(G)...Let G= (V, E) be a graph and A(G) is the collection of all minimal equitable dominating set of G. The middle equitable dominating graph of G is the graph denoted by Med(G) with vertex set the disjoint union of V∪A(G) and (u, v) is an edge if and only if u ∩ v ≠ φ whenever u, v ∈ A(G) or u ∈ v whenever u ∈ v and v ∈ A(G) . In this paper, characterizations are given for graphs whose middle equitable dominating graph is connected and Kp∈Med(G) . Other properties of middle equitable dominating graphs are also obtained.展开更多
In this paper, we investigated the code over GF(2) which is generated by the incidence matrix of the symmetric (2,4) - net D. By computer search, we found that this binary code of D has rank 13 and the minimum distanc...In this paper, we investigated the code over GF(2) which is generated by the incidence matrix of the symmetric (2,4) - net D. By computer search, we found that this binary code of D has rank 13 and the minimum distance is 8.展开更多
文摘Let?G=(V,E)? be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two vertices?u, v ∈ V(G)? are?φ -equitable if|φ(u)-φ(v)|≤1.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.
文摘In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ,?,?NCN-energy for some standard graphs is obtained and an upper bound for ?is found when G is a strongly regular graph. Also the relation between common neigh-bourhood energy and non-common neighbourhood energy of a graph is established.
文摘Let G= (V, E) be a graph and A(G) is the collection of all minimal equitable dominating set of G. The middle equitable dominating graph of G is the graph denoted by Med(G) with vertex set the disjoint union of V∪A(G) and (u, v) is an edge if and only if u ∩ v ≠ φ whenever u, v ∈ A(G) or u ∈ v whenever u ∈ v and v ∈ A(G) . In this paper, characterizations are given for graphs whose middle equitable dominating graph is connected and Kp∈Med(G) . Other properties of middle equitable dominating graphs are also obtained.
文摘In this paper, we investigated the code over GF(2) which is generated by the incidence matrix of the symmetric (2,4) - net D. By computer search, we found that this binary code of D has rank 13 and the minimum distance is 8.
