摘要
In this paper authors have obtained a new necessary and sufficient condition for a graph G to be a geodetic graph. Let g : E --> Z(+) be a function from the set of edges of a graph G to the set of nonnegative integers and let g(G) denote the graph obtained from G by replacing each edge e is an element of E by a suspended are (path) P-g(e+2) of length g(e) + 1. and by using this condition, established a criterion for a function g to be a function which can generate a new geodetic block g(G) from a given geodetic block G.
In this paper authors have obtained a new necessary and sufficient condition for a graph G to be a geodetic graph. Let g : E --> Z(+) be a function from the set of edges of a graph G to the set of nonnegative integers and let g(G) denote the graph obtained from G by replacing each edge e is an element of E by a suspended are (path) P-g(e+2) of length g(e) + 1. and by using this condition, established a criterion for a function g to be a function which can generate a new geodetic block g(G) from a given geodetic block G.
