Rank Reduction of Oriented Graphs by Vertex and Edge Deletions
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DOI: 10.1007/s00453-017-0340-2
Abstract: In this paper we continue our study of graph modification problems defined by reducing the rank of the adjacency matrix of the given graph, and extend our results from undirected graphs to modifying the rank… read more here.
Keywords: adjacency matrix; edge; deletion; oriented graphs ... See more keywords
Graph-Counting Polynomials for Oriented Graphs
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DOI: 10.1007/s10955-018-2137-3
Abstract: If $$\mathcal{F}$$F is a set of subgraphs F of a finite graph E we define a graph-counting polynomial $$p_\mathcal{F}(z)=\sum _{F\in \mathcal{F}}z^{|F|}$$pF(z)=∑F∈Fz|F| In the present note we consider oriented graphs and discuss some cases where $$\mathcal{F}$$F… read more here.
Keywords: graph counting; oriented graphs; counting polynomials; polynomials oriented ... See more keywords
Tricyclic Oriented Graphs with Maximal Skew Energy
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DOI: 10.1007/s40840-016-0304-8
Abstract: Let $$G^\sigma $$Gσ be an oriented graph obtained by assigning an orientation $$\sigma $$σ to the edge set of a simple undirected graph G. Let $$S(G^\sigma )$$S(Gσ) be the skew-adjacency matrix of $$G^\sigma $$Gσ. The… read more here.
Keywords: skew energy; oriented graphs; tricyclic oriented; maximal skew ... See more keywords