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Let \(\mathcal{T}=(V,\mathcal{E})\) be a 3-uniform linear hypertree. We consider a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\). We are interested in the following problem. We have to decide whether there exists a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\) of the hypertree \(\mathcal{T}\), with hyperedge densities satisfying some conditions, such that the hypertree \(\mathcal{T}\) does not...
In this paper we show some properties of the eccentric distance sum index which is defined as follows \(\xi^{d}(G)=\sum_{v \in V(G)}D(v) \varepsilon(v)\). This index is widely used by chemists and biologists in their researches. We present a lower bound of this index for a new class of graphs.
The Ramsey number \(R(G, H)\) for a pair of graphs \(G\) and \(H\) is defined as the smallest integer \(n\) such that, for any graph \(F\) on \(n\) vertices, either \(F\) contains \(G\) or \(\overline{F}\) contains \(H\) as a subgraph, where \(\overline{F}\) denotes the complement of \(F\). We study Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths and determine these...
In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid...
In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum, Vol. 7 (2002) no. 26, 1289–1294]. The adjacent eccentric distance sum index of the graph \(G\) is defined as\[\xi ^{sv} (G)= \sum_{v\in...
Let \(ex(n, G)\) denote the maximum number of edges in a graph on \(n\) vertices which does not contain \(G\) as a subgraph. Let \(P_i\) denote a path consisting of \(i\) vertices and let \(mP_i\) denote \(m\) disjoint copies of \(P_i\). In this paper we count \(ex(n, 3P_4)\).
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