Let N denote the set of positive integers.The sum graph G^+(S)of a finite subset S(?)N is the graph(S,E)with uv∈E if and only if u+v∈S.A graph G is said to be a sum graph if it is isomorphic to the sum graph of som...Let N denote the set of positive integers.The sum graph G^+(S)of a finite subset S(?)N is the graph(S,E)with uv∈E if and only if u+v∈S.A graph G is said to be a sum graph if it is isomorphic to the sum graph of some SN.By using the set Z of all integers instead of N,we obtain the definition of the integral sum graph.A graph G=(V,E)is a rood sum graph if there exists a positive integer z and a labelling,λ,of the vertices of G with distinct elements from {0,1,2,...,z-1} so that uv∈E if and only if the sum,modulo z,of the labels assigned to u and v is the label of a vertex of G.In this paper,we prove that flower tree is integral sum graph.We prove that Dutch m-wind-mill(D_m)is integral sum graph and rood sum graph,and give the sum number of D_m.展开更多
文摘Let N denote the set of positive integers.The sum graph G^+(S)of a finite subset S(?)N is the graph(S,E)with uv∈E if and only if u+v∈S.A graph G is said to be a sum graph if it is isomorphic to the sum graph of some SN.By using the set Z of all integers instead of N,we obtain the definition of the integral sum graph.A graph G=(V,E)is a rood sum graph if there exists a positive integer z and a labelling,λ,of the vertices of G with distinct elements from {0,1,2,...,z-1} so that uv∈E if and only if the sum,modulo z,of the labels assigned to u and v is the label of a vertex of G.In this paper,we prove that flower tree is integral sum graph.We prove that Dutch m-wind-mill(D_m)is integral sum graph and rood sum graph,and give the sum number of D_m.
