In this paper we learn the new idea of forcing total outer independent edge geodetic number a graph. Let G be connected graph and R minimum set G. A subset L ⊆ is known as for if unique containing L. cardinality R. The denoted by (G) = min , where taken over all in Some general properties satisfied concept are studied. It shown that any couple integers l, m with0 < l ≤ − 4, there exists such .

For two vertices u and v of a graph G, the closed interval I[u, v] consists of u, v, and all vertices lying in some u − v geodesic in G. If S is a set of vertices of G, then I[S] is the union of all sets I[u, v] for u, v ∈ S. If I[S] = V (G), then S is a geodetic set for G. The geodetic number g(G) is the minimum cardinality of a geodetic set. A set S of vertices in a graph G is uniform if the ...

Buckley and Harary introduced several graphical invariants related to convexity theory, such as the geodetic number of a graph. These invariants have been the subject of much study and their determination has been shown to be NP -hard. We use the probabilistic method developed by Erdös to determine the asymptotic behavior of the geodetic number of random graphs with fixed edge probability. As a...

For a connected graph G of order n, a set S ⊆ V (G) is a geodetic set of G if each vertex v ∈ V (G) lies on a x-y geodesic for some elements x and y in S. The minimum cardinality of a geodetic set of G is defined as the geodetic number of G, denoted by g(G). A geodetic set of cardinality g(G) is called a g-set of G. A set S of vertices of a connected graph G is an open geodetic set of G if for ...

We propose a new filtering algorithm for the cumulative constraint. It applies the Edge-Finding, the Extended-Edge-Finding and the Time-Tabling rules in O(kn logn) where k is the number of distinct task heights. By a proper use of tasks decomposition, it enforces the Time-Tabling rule and the Time-Table Extended-Edge-Finding rule. Thus our algorithm improves upon the best known Extended-Edge-Fi...

the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

A digraph G = (V, E) with diameter D is said to be s-geodetic, for 1 ≤ s ≤ D, if between any pair of (not necessarily different) vertices x, y ∈ V there is at most one x → y path of length ≤ s. Thus, any loopless digraph is at least 1-geodetic. A similar definition applies for a graph G, but in this case the concept is closely related to its girth g, for then G is s-geodetic with s = b(g − 1)/2...

The edge C4 graph of a graph G, E4(G) is a graph whose vertices are the edges of G and two vertices in E4(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C4. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C4 graphs are isomorphic. We study the relationship between the diameter, radius and domina...