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Completeness-Resolvable Graphs [PDF]
Graphs and Combinatorics, 2022 Given a connected graph $G=(V(G), E(G))$, the length of a shortest path from a vertex $u$ to a vertex $v$ is denoted by $d(u,v)$. For a proper subset $W$ of $V(G)$, let $m(W)$ be the maximum value of $d(u,v)$ as $u$ ranging over $W$ and $v$ ranging over $V(G)\setminus W$. The proper subset $W=\{w_1,\ldots,w_{|W|}\}$ is a {\em completeness-resolving set}
Min Feng, Xuanlong Ma, Huiling Xu
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JTAM (Jurnal Teori dan Aplikasi Matematika), 2022 The research in graph theory has been widened by combining it with ring. In this paper, we introduce the definition of a non-braid graph of a ring. The non-braid graph of a ring R, denoted by YR, is a simple graph with a vertex set R\B(R), where B(R) is
Era Setya Cahyati +3 more
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Domination number of middle graphs [PDF]
Transactions on Combinatorics, 2023 In this paper, we study the domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph G. We also compute the domination number of some families of graphs such as star graphs, double start graphs,
Farshad Kazemnejad +3 more
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Decomposition of complete graphs into small graphs [PDF]
Opuscula Mathematica, 2010 In 1967, A. Rosa proved that if a bipartite graph \(G\) with \(n\) edges has an \(\alpha\)-labeling, then for any positive integer \(p\) the complete graph \(K_{2np+1}\) can be cyclically decomposed into copies of \(G\).
Dalibor Froncek
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Theory and Applications of Graphs, 2020 In his classical paper [14], Rosa introduced a hierarchical series of labelings called ρ, σ, β and α labeling as a tool to settle Ringel’s Conjecture which states that if T is any tree with m edges then the complete graph K2m+1 can be decomposed into 2m +
G. Sethuraman, M. Sujasree
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An Improvement of the Lower Bound on the Minimum Number of ≤k-Edges
Mathematics, 2021 In this paper, we improve the lower bound on the minimum number of ≤k-edges in sets of n points in general position in the plane when k is close to n2.
Javier Rodrigo +3 more
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Interval edge-coloring: A model of curriculum scheduling
AKCE International Journal of Graphs and Combinatorics, 2020 Considering the appointments that teachers plan to teach some courses for specific classes, the problem is to schedule the curriculum such that the time for each teacher is consecutive.
Zehui Shao +4 more
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Computational graph completion
Research in the Mathematical Sciences, 2022 34 pages.
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Ultrametrics and Complete Multipartite Graphs
Theory and Applications of Graphs, 2022 Let \((X, d)\) be a semimetric space and let \(G\) be a graph. We say that \(G\) is the diametrical graph of \((X, d)\) if \(X\) is the vertex set of \(G\) and the adjacency of vertices \(x\) and \(y\) is equivalent to the equality \(\diam X = d(x, y)\).
Viktoriia Viktorivna Bilet +2 more
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Factorizations of complete graphs into tadpoles
AKCE International Journal of Graphs and Combinatorics, 2020 A tadpole (also a canoe paddle or lollipop) is a graph that arises from a cycle and a path by gluing a terminal vertex of the path to an arbitrary vertex of the cycle.
Michael Kubesa, Tom Raiman
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