A simple graph G=(V,E)is said to be vertex Euclidean if there exists a bijection f from V to{1,2,...,|V|}such that f(u)+f(v)>f(w)for each C3 subgraph with vertex set{u,v,w},where f(u)<f(v)<f(w).The vertex Euc...A simple graph G=(V,E)is said to be vertex Euclidean if there exists a bijection f from V to{1,2,...,|V|}such that f(u)+f(v)>f(w)for each C3 subgraph with vertex set{u,v,w},where f(u)<f(v)<f(w).The vertex Euclidean deficiency of a graph G,denotedμv Euclid(G),is the smallest positive integer n such that G∪N_(n) is vertex Euclidean.In this paper,we introduce some methods for deriving the vertex Euclidean properties of some simple graphs.展开更多
文摘A simple graph G=(V,E)is said to be vertex Euclidean if there exists a bijection f from V to{1,2,...,|V|}such that f(u)+f(v)>f(w)for each C3 subgraph with vertex set{u,v,w},where f(u)<f(v)<f(w).The vertex Euclidean deficiency of a graph G,denotedμv Euclid(G),is the smallest positive integer n such that G∪N_(n) is vertex Euclidean.In this paper,we introduce some methods for deriving the vertex Euclidean properties of some simple graphs.
