We prove that every connected graph with girth at least 4 and s vertices whose degree differs from 2 contains a spanning tree with atleast $ \\\frac{1}{3}\\\left( {s - 2} ight) $ + 2 leaves. We describe series of examples showing that this bound is tight. This result, together...
A graph is unicyclic if and only if it is connected and has size equal to its order. We shall by Hn,k denote the unicyclic graph constructed by attaching n-k leaves to one vertex on a cycle of length k. The Fibonacci numbers 0,1,1,2,3,5,8,13,21,34,… are defined recursively ...
0282: tree egg 0283: stone egg 0284: sky egg 0285: winning ticket 0286: grand-prize ticket 0287: forest wall 0288: forest floor 0289: mush bed 0290: mush dresser 0291: mush closet 0292: mush chair 0293: mush stool 0294: mush table ...
On the Wiener polarity index of trees with maximum degree or given number of leaveswiener polarity indextreemaximum degreeleaveThe Wiener polarity index W_P(G) of a graph G = (V, E) is the number of unordered pairs of vertices {u, v} of G such that the distance d_G(u, v) = 3...
A path-component of a graph is a connected component that is a path. Theorem 5 Let F be a forest with v1 vertices of degree 1, v2 vertices of degree 2 and p path-components. Then psn(F)=v1+v2−p. Corollary 6 The smallest path separation number for a tree T on n vertices ...
'Return' statement in a Function,Get,or Operator must return a value...Question "An error occurred during local reporting processing. Object reference not set to an instance of an object." "Define query parameters" popup in Dataset properties -> Refersh field, not displayed for Sps in ...
Seamless green leaves with little white flower background Free with trial Green paper leaf and water drops Free with trial Illustration vector, House on peaceful island, Sun with blue sky Free with trial Illustration Fantasy of Tree house on the blue sky background ...
A near-isogenic line, NIL-TAW1, was developed to evaluate its effects. In comparison with the recurrent parent R498, NIL-TAW1 showed increased panicle length (14.0%), number of secondary branches (20.9%) and GNP (22.0%), and the final grain yield per plant of NIL-TAW1 was increased ...
A k-tree is a graph defined inductively in the following way: the complete graph Kk is a k-tree, and if G is a k-tree, then the graph resulting from adding a new vertex adjacent to k vertices inducing a Kk in G is also a k-tree. This paper examines the book-embedding problem ...
There are (35)2−30 leaves on a tree. What is the total number of leaves on the tree? Evaluating an Expression We have to evaluate the expression given. The expression contains exponential terms and, therefore, we need to make use of the various rules of expone...