Results 11 to 20 of about 4,003 (201)
On the spread of outerplanar graphs
Special Matrices, 2022 The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large nn, the nn-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with Ω(n ...
Gotshall Daniel +2 more
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Outerplanar graph drawings with few slopes [PDF]
Computational Geometry, 2014 We consider straight-line outerplanar drawings of outerplanar graphs in which a small number of distinct edge slopes are used, that is, the segments representing edges are parallel to a small number of directions.
Bartosz Walczak +16 more
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Planar, Outerplanar, and Toroidal Graphs of the Generalized Zero-Divisor Graph of Commutative Rings
Journal of Mathematics, 2021 Let A be a commutative ring with unity and let set of all zero divisors of A be denoted by ZA. An ideal ℐ of the ring A is said to be essential if it has a nonzero intersection with every nonzero ideal of A. It is denoted by ℐ≤eA.
Abdulaziz M. Alanazi +2 more
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A note on outerplanarity of product graphs [PDF]
Applicationes Mathematicae, 1991 Summary: We prove necessary and sufficient conditions for the outerplanarity of the Cartesian product and Kronecker product of graphs. In our discussions, the class of almost bipartite graphs is defined and we show that if \(G\) is an almost bipartite graph, then it is a minor of \(G\times K_ 2\). We conjecture that this is true for all graphs.
Pranava K. Jha, Giora Slutzki
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Equitable colorings of outerplanar graphs
Discrete Mathematics, 2002 A proper vertex coloring of a graph \(G\) is said to be equitable if the sizes of any two color classes differ by at most 1. It was conjectured by \textit{H. P. Yap} and \textit{Y. Zhang} [Bull. Inst. Math., Acad. Sin. 25, 143-149 (1997; Zbl 0882.05054)] that every outerplanar graph with maximum degree at most \(\Delta\) admits an equitable \(k ...
Alexandr Kostochka
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Pathlength of Outerplanar Graphs
, 2022 A path-decomposition of a graph G = (V, E) is a sequence of subsets of V , called bags, that satisfy some connectivity properties. The length of a path-decomposition of a graph G is the greatest distance between two vertices that belong to a same bag and the pathlength, denoted by pl(G), of G is the smallest length of its path-decompositions.
Thomas Dissaux, Nicolas Nisse
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COLORING THE SQUARE OF AN OUTERPLANAR GRAPH [PDF]
Taiwanese Journal of Mathematics, 2006 Let $G$ be an outerplanar graph with maximum degree $\Delta(G)\ge 3$. We prove that the chromatic number $\chi(G^2)$ of the square of $G$ is at most $\Delta(G)+2$. This confirms a conjecture of Wegner [8] for outerplanar graphs. The upper bound can be further reduced to the optimal value $\Delta(G)+1$ when $\Delta(G)\ge 7$.
Ko‐Wei Lih, Weifan Wang
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Geometric assortative growth model for small-world networks. [PDF]
ScientificWorldJournal, 2014 It has been shown that both humanly constructed and natural networks are often characterized by small‐world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small‐world networks. The model displays both tunable small‐world phenomenon and tunable assortativity.
Shang Y.
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Metric Dimension of Maximal Outerplanar Graphs [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2021 25 pages, 16 ...
M. Claverol +6 more
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Free Choosability of Outerplanar Graphs [PDF]
Graphs and Combinatorics, 2015 A graph G is free (a, b)-choosable if for any vertex v with b colors assigned and for any list of colors of size a associated with each vertex $$u\ne v$$u?v, the coloring can be completed by choosing for u a subset of b colors such that adjacent vertices are colored with disjoint color sets.
Yves Aubry +2 more
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