# Characterization of Line Sidigraphs

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Seymour's Second Neighborhood Conjecture asserts that every oriented graph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. It is proved for tournaments, tournaments missing a matching and tournaments missing a generalized star. We...

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Up to isomorphism, there are two tournaments, called diamonds, on 4 vertices and containing a unique 3-cycle. If T is a tournament containing at least a diamond, the diamonds' support of T is the intersection of all the subsets X of V ( T) such that the sub-tournament T [ X] of T, induced by X,...

- Zero Divisors Among Digraphs. Hammack, Richard; Smith, Heather // Graphs & Combinatorics;Jan2014, Vol. 30 Issue 1, p171
A digraph C is called a zero divisor if there exist non-isomorphic digraphs A and B for which $${A \times C \cong B \times C}$$ , where the operation is the direct product. In other words, C being a zero divisor means that cancellation property $${A \times C \cong B \times C \Rightarrow A \cong...

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A digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x0x1 x2x3 of length 3, x0 and x3 are adjacent (resp. x0 dominates x3). CÃ©sar HernÃ¡ndez-Cruz conjectured that if D is a 3-quasi-transitive digraph, then the underlying graph of D, UG(D), admits a 3-transitive orientation....

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No abstract available.

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A graph property is any class of graphs that is closed under isomorphisms. A graph property P is hereditary if it is closed under taking subgraphs; it is compositive if for any graphs G, G âˆˆ P there exists a graph G âˆˆ P containing both G and G as subgraphs. Let H be any given graph on...

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A graph G is { K, K + e}-free if G contains no induced subgraph isomorphic to K or K + e. In this paper, we show that G has a path which is either hamiltonian or of length at least 2 Î´ + 2 if G is a connected { K, K + e}-free graph on at least 7 vertices.

- The signless Laplacian spectral radius of C4-free graphs with even order. LI Guang-bin // Basic Sciences Journal of Textile Universities / Fangzhi Gaoxia;jun2013, Vol. 26 Issue 2, p171
Let G be a simple graph, the matrix Q(G)=D(G)+A(G) denotes the signless Laplacian matrix of G, where D(G) and A(G) denote the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. In this paper, we prove that if G is a C4-free graph (a graph contains no subgraphs...