Results 11 to 20 of about 771 (82)
On the 12-Representability of Induced Subgraphs of a Grid Graph
Discussiones Mathematicae Graph Theory, 2022 The notion of a 12-representable graph was introduced by Jones, Kitaev, Pyatkin and Remmel in [Representing graphs via pattern avoiding words, Electron. J. Combin. 22 (2015) #P2.53].
Chen Joanna N., Kitaev Sergey
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ON THE RAINBOW NEIGHBOURHOOD NUMBER OF MYCIELSKI TYPE GRAPHS
International Journal of Apllied Mathematics, 2019 A rainbow neighbourhood of a graph G is the closed neighbourhood N [v] of a vertex v ∈ V (G) which contains at least one colored vertex of each color in the chromatic coloring C of G. Let G be a graph with a chromatic coloring C defined on it. The number
N. Sudev, C. Susanth, S. Kalayathankal
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Maximum nullity and zero forcing of circulant graphs
Special Matrices, 2020 The zero forcing number of a graph has been applied to communication complexity, electrical power grid monitoring, and some inverse eigenvalue problems.
Duong Linh +4 more
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One-Three Join: A Graph Operation and Its Consequences
Discussiones Mathematicae Graph Theory, 2017 In this paper, we introduce a graph operation, namely one-three join. We show that the graph G admits a one-three join if and only if either G is one of the basic graphs (bipartite, complement of bipartite, split graph) or G admits a constrained ...
Shalu M.A., Devi Yamini S.
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On the edge set of graphs of lattice paths
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 61, Page 3291-3299, 2004., 2004 This note explores a new family of graphs defined on the set of paths of the m × n lattice. We let each of the paths of the lattice be represented by a vertex, and connect two vertices by an edge if the corresponding paths share more than k steps, where k is a fixed parameter 0 = k = m + n. Each such graph is denoted by G(m, n, k).
Steven Klee, Lara Pudwell, Rick Gillman
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On Accurate Domination in Graphs
Discussiones Mathematicae Graph Theory, 2019 A dominating set of a graph G is a subset D ⊆ VG such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of
Cyman Joanna +2 more
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Minimally Strong Subgraph (k,ℓ)-Arc-Connected Digraphs
Discussiones Mathematicae Graph Theory, 2022 Let D = (V,A) be a digraph of order n, S a subset of V of size k and 2 ≤ k ≤ n. A subdigraph H of D is called an S-strong subgraph if H is strong and S ⊆ V (H). Two S-strong subgraphs D1 and D2 are said to be arc-disjoint if A(D1) ∩ A(D2) = ∅.
Sun Yuefang, Jin Zemin
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, 2011 In this note we define two generalizations of the line graph and obtain some results.
Permi, S. +2 more
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Old and new generalizations of line graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 29, Page 1509-1521, 2004., 2004 Line graphs have been studied for over seventy years. In 1932, H. Whitney showed that for connected graphs, edge‐isomorphism implies isomorphism except for K3 and K1,3. The line graph transformation is one of the most widely studied of all graph transformations.
Jay Bagga
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Characterizing symmetric diametrical graphs of order 12 and diameter 4
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 3, Page 145-149, 2002., 2002 A diametrical graph G is said to be symmetric if d(u,v)+d(v,u¯)=d(G) for all u, v ∈ V(G), where u¯ is the buddy of u. If moreover, G is bipartite, then it is called an S‐graph. It would be shown that the Cartesian product K2 × C6 is not only the unique S‐graph of order 12 and diameter 4, but also the unique symmetric diametrical graph of order 12 and ...
S. Al-Addasi, H. Al-Ezeh
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