Track layouts of graphs.
Dujmović, Vida, Pór, Attila, Wood, David R. (2004)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Dujmović, Vida, Pór, Attila, Wood, David R. (2004)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Dujmović, Vida, Wood, David R. (2004)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Barequet, Gill, Goodrich, Michael T., Riley, Chris (2004)
Journal of Graph Algorithms and Applications
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Morin, Pat, Wood, David R. (2004)
Journal of Graph Algorithms and Applications
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Wood, David R. (2006)
The Electronic Journal of Combinatorics [electronic only]
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Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson (2013)
Discussiones Mathematicae Graph Theory
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For a fixed graph F, a graph G is F-saturated if there is no copy of F in G, but for any edge e ∉ G, there is a copy of F in G + e. The minimum number of edges in an F-saturated graph of order n will be denoted by sat(n, F). A graph G is weakly F-saturated if there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n will be denoted by wsat(n, F). The graphs...
Cariolaro, David, Fu, Hung-Lin (2009)
The Electronic Journal of Combinatorics [electronic only]
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A.P. Santhakumaran, S. Athisayanathan (2010)
Discussiones Mathematicae Graph Theory
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For two vertices u and v in a graph G = (V,E), the detour distance D(u,v) is the length of a longest u-v path in G. A u-v path of length D(u,v) is called a u-v detour. A set S ⊆V is called an edge detour set if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn₁(G) of G is the minimum order of its edge detour sets and any edge detour set of order dn₁(G) is an edge detour basis of G. A connected graph G is called an edge detour graph if it has...
Muhammad Javaid (2014)
Discussiones Mathematicae Graph Theory
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In 1980, Enomoto et al. proposed the conjecture that every tree is a super (a, 0)-edge-antimagic total graph. In this paper, we give a partial sup- port for the correctness of this conjecture by formulating some super (a, d)- edge-antimagic total labelings on a subclass of subdivided stars denoted by T(n, n + 1, 2n + 1, 4n + 2, n5, n6, . . . , nr) for different values of the edge- antimagic labeling parameter d, where n ≥ 3 is odd, nm = 2m−4(4n+1)+1, r ≥ 5 and 5 ≤ m ≤ r.
Vajk Szécsi (2013)
Open Mathematics
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A nearly sharp lower bound on the length of the longest trail in a graph on n vertices and average degree k is given provided the graph is dense enough (k ≥ 12.5).
Sana Javed, Mujtaba Hussain, Ayesha Riasat, Salma Kanwal, Mariam Imtiaz, M. O. Ahmad (2017)
Open Mathematics
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An edge-magic total labeling of an (n,m)-graph G = (V,E) is a one to one map λ from V(G) ∪ E(G) onto the integers {1,2,…,n + m} with the property that there exists an integer constant c such that λ(x) + λ(y) + λ(xy) = c for any xy ∈ E(G). It is called super edge-magic total labeling if λ (V(G)) = {1,2,…,n}. Furthermore, if G has no super edge-magic total labeling, then the minimum number of vertices added to G to have a super edge-magic total labeling, called super edge-magic deficiency...
Jaroslav Ivančo, Stanislav Jendrol' (2006)
Discussiones Mathematicae Graph Theory
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A total edge-irregular k-labelling ξ:V(G)∪ E(G) → {1,2,...,k} of a graph G is a labelling of vertices and edges of G in such a way that for any different edges e and f their weights wt(e) and wt(f) are distinct. The weight wt(e) of an edge e = xy is the sum of the labels of vertices x and y and the label of the edge e. The minimum k for which a graph G has a total edge-irregular k-labelling is called the total edge irregularity strength of G, tes(G). In this paper we prove that...
Felsner, Stefan, Massow, Mareike (2008)
Journal of Graph Algorithms and Applications
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