A given graph H is called realizable by a graph G if G [ N (v) ] H for every vertex v of G. The Trahtenbrot–Zykov problem says that which graphs are realizable. We consider a problem somewhat opposite in a more general setting. Let t be a positive integer. We characterize all ...
If {eq}\, {\bf c} = \|{\bf a}\|{\bf b} + \|{\bf b}\|{\bf a}, \, {/eq} where {eq}\, {\bf a}, {\bf b},\, {/eq} and {eq}\, {\bf c}\, {/eq} are all nonzero vectors, ...
In turn, beginning with white, the players position their men one at a time on unoccupied vertices of G . When all men are placed, the players take turns moving a man of their color along an edge to an unoccupied adjacent vertex (again beginning with white). A player wins if his ...
In a graph G a vertex v dominates all its neighbors and itself. A set D of vertices of G is (vertex) dominating set if each vertex of G is dominated by at ... BJ Ebrahimi,N Jahanbakht,ES Mahmoodian - 《Discrete Mathematics》 ...
The formula used to find the area bounded by the curves is {eq}\displaystyle A = \dfrac{1}{2} \int_a^b \left[ f(\theta) \right]^2 d\theta {/eq}. We use the application of integration to find the area. Answer and Explanati...
The first line will look likeV N, whereVis the number of vertices in the graph, andNis the period of the edge weights. Following that, there will be one line per edge, in the formatis an integer representing the source vertex of the edge,vtan integerrepresenting the target vertex of th...
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The function f(x) is increasing where a first derivation is positive f'(x)0. For instance, let's find an interval where the functionf(x) =x^2 - 5x is...Become a member and unlock all Study Answers Start today. Try it now Create an account Ask a question Our experts can...
求高手帮忙翻译下英文文献in this paper,we consider only simple connected graphs and follow the notationof [1].Let G be a simple graph with vertex set V(G) and edge set E(G). Theadjacency matrix of G is A(G) = (J), where J = 1 if two vertic
can be interpreted as making an infinite walk in the directed graph \(g = (s,e)\) , where \(e = \{(x,y)\mid x\in s { and} y\in a(x)\}\) . in this paper, whenever we refer to an ordered pair ( x , y ) as an edge , it is implicit that \(x\in s\) and...