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Graph Equations for Line Graphs, Jump Graphs, Middle Graphs, Splitting Graphs and Line Splitting Graphs [PDF]
Mapana Journal of Sciences, 2010 For a graph G, let G, L(G), J(G) S(G), L,(G) and M(G) denote Complement, Line graph, Jump graph, Splitting graph, Line splitting graph and Middle graph respectively. In this paper, we solve the graph equations L(G) =S(H), M(G) = S(H), L(G) = LS(H), M(G) =LS(H), J(G) = S(H), M(G) = S(H), J(G) = LS(H) and M(G) = LS(G).
B. Basavanagoud, Veena Mathad
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On the Wiener and Harary Index of Splitting Graphs
European Journal of Pure and Applied Mathematics, 2022 Let G=(V,E) be a simple undirected graph and S⊆V. The S-splitting Graph of G denoted by Γ(G,S)=Γ is obtained by replicating the vertices x in S as well as the edges adjacent to it.
Francis Joseph H Campeña
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Biclique graphs of split graphs
Discrete Applied Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marina Groshaus +2 more
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Vertex Splitting and the Recognition of Trapezoid Graphs [PDF]
Discrete Applied Mathematics, 2011 Trapezoid graphs are the intersection family of trapezoids where every trapezoid has a pair of opposite sides lying on two parallel lines. These graphs have received considerable attention and lie strictly between permutation graphs (where the trapezoids
George Mertzios, Derek Corneil
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SIAM Journal on Discrete Mathematics, 1988
The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This concept is at the core of a new bounding technique for graph covering problems and has furnished the best known bounds for the problem of perfect hashing.
KORNER, JANOS, K. Marton
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The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This concept is at the core of a new bounding technique for graph covering problems and has furnished the best known bounds for the problem of perfect hashing.
KORNER, JANOS, K. Marton
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Graphs and Combinatorics, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nicholas Korpelainen +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nicholas Korpelainen +2 more
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Eccentricity Splitting Graph of a Graph
Journal of Discrete Mathematical Sciences and Cryptography, 2021Let G = (V, E) be any connected graph with for all uj, uk ∈ Si if e(uj) = e(uk)(1 ≤ i ≤ t) with each | Si|≥ 2 and .
Nivedha Baskar
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Splitting and Contractible Edges in 4-Connected Graphs
Journal of Combinatorial Theory Series B, 2003 Let G be a graph and let x be a vertex of degree four with NG(x)={a,b,c,d}. Then the operation of deleting x and adding the edges ab and cd is called splitting at x.
Saito, Akira
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IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2004
Phylogenetic trees correspond one-to-one to compatible systems of splits and so splits play an important role in theoretical and computational aspects of phylogeny. Whereas any tree reconstruction method can be thought of as producing a compatible system of splits, an increasing number of phylogenetic algorithms are available that compute split systems
Andreas W. M. Dress, Daniel H. Huson
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Phylogenetic trees correspond one-to-one to compatible systems of splits and so splits play an important role in theoretical and computational aspects of phylogeny. Whereas any tree reconstruction method can be thought of as producing a compatible system of splits, an increasing number of phylogenetic algorithms are available that compute split systems
Andreas W. M. Dress, Daniel H. Huson
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