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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
core +8 more sources
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
doaj +3 more sources
Large Induced Acyclic and Outerplanar Subgraphs of 2-Outerplanar Graph [PDF]
Graphs and Combinatorics, 2017 Albertson and Berman conjectured that every planar graph has an induced forest on half of its vertices. The best known lower bound, due to Borodin, is that every planar graph has an induced forest on two fifths of its vertices.
Glencora Borradaile +2 more
semanticscholar +6 more sources
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.
Ko‐Wei Lih, Weifan Wang
semanticscholar +5 more sources
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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Bipolar fuzzy outerplanar graphs approach in image shrinking [PDF]
Scientific ReportsBipolar fuzzy outerplanar graphs are interesting and significant subclasses within the broader field of fuzzy graph theory. In this paper, bipolar fuzzy outerplanar graphs, and its properties are introduced.
Deivanai Jaisankar +3 more
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The 2-center Problem in Maximal Outerplanar Graph [PDF]
arXiv.org, 2022 We consider the problem of computing 2-center in maximal outerplanar graph. In this problem, we want to find an optimal solution where two centers cover all the vertices with the smallest radius. We provide the following result.
Hsiu-Fu Yeh
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On k-edge-magic labelings of maximal outerplanar graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2015 Let G be a graph with vertex set V and edge set E such that |V|=p and |E|=q. We denote this graph by (p,q)-graph. For integers k≥0, define a one-to-one map f from E to {k,k+1,…,k+q−1} and define the vertex sum for a vertex v as the sum of the labels of ...
Gee-Choon Lau +3 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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Edge-group choosability of outerplanar and near-outerplanar graphs [PDF]
Transactions on Combinatorics, 2020 Let $\chi_{gl}(G)$ be the {\it{group choice number}} of $G$. A graph $G$ is called {\it{edge-$k$-group choosable}} if its line graph is $k$-group choosable. The {\it{group-choice index}} of $G$, $\chi'_{gl}(G)$, is the smallest $k$ such that $G$ is edge-$
Amir Khamseh
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