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111.
《Discrete Mathematics》2022,345(10):113028
We prove that every 52-connected line graph of a rank 3 hypergraph is Hamiltonian. This is the first result of this type for hypergraphs of bounded rank other than ordinary graphs. 相似文献
112.
113.
The authors introduce a notion of a weak graph map homotopy (they call it
M-homotopy), discuss its properties and applications. They prove that the weak graph
map homotopy equivalence between graphs coincides with the graph homotopy equivalence
defined by Yau et al in 2001. The difference between them is that the weak graph map
homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over
the graph homotopy transformation. As its applications, they investigate the mapping
class group of a graph and the 1-order MP-homotopy group of a pointed simple graph.
Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is
invariant up to the weak graph map homotopy equivalence. 相似文献
114.
115.
设$ G $ 是一个$ n $ 阶$ k $ 圈图, $ k $ 圈图为边数等于顶点数加$ k-1 $ 的简单连通图。$ \mu_{1}(G) $ 、$ \mu_{2}(G) $ 分别记为图$ G $ 的Laplace矩阵的最大特征值和次大特征值, 图$ G $ 的Laplace分离度定义为$ S_{L}(G)=\mu_{1}(G)-\mu_{2}(G) $ 。本文研究了给定阶数的$ k $ 圈图的最大Laplace分离度, 并刻画了相应的极图, 其结果推广了已有当$ k=1, 2, 3 $ 时的结论。 相似文献
116.
We introduce an impartial combinatorial game on Steiner triple systems called Next One to Fill Is the Loser (Nofil ). Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. By computing nim-values, we determine optimal strategies for Nofil on all Steiner triple systems up to order 15 and a sampling for orders 19, 21 and 25. The game Nofil can be thought of in terms of play on a corresponding hypergraph which will become a graph during play. At that point Nofil is equivalent to playing the game Node Kayles on the graph. We prove necessary conditions and sufficient conditions for a graph to reached playing Nofil. We conclude that the complexity of determining the outcome of the game Nofil on Steiner triple systems is PSPACE-complete for randomized reductions. 相似文献
117.
The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data. This is an NP-hard problem that can be relaxed in the spectral graph theory, where the optimal cuts of a graph are related to the eigenvalues of graph 1-Laplacian. In this paper, we first give new notations to describe the paths, among critical eigenvectors of the graph 1-Laplacian, realizing sets with prescribed genus. We introduce the pseudo-orthogonality to characterize m3(G), a special eigenvalue for the graph 1-Laplacian. Furthermore, we use it to give an upper bound for the third graph Cheeger constant h3(G), that is, h3(G) 6 m3(G). This is a first step for proving that the k-th Cheeger constant is the minimum of the 1-Laplacian Raylegh quotient among vectors that are pseudo-orthogonal to the vectors realizing the previous k - 1 Cheeger constants. Eventually, we apply these results to give a method and a numerical algorithm to compute m3(G), based on a generalized inverse power method. 相似文献
118.
On bandwidth sums of graphs 总被引:1,自引:0,他引:1
ONBANDWIDTHSUMSOFGRAPHSYAOBING(姚兵);WANGJIANFANG(王建方)(DepartmentofMathematics,NorihwesteternNormalUniversity,Lanzhou730070,Chi... 相似文献
119.
Robert W. Baddeley 《Journal of Algebraic Combinatorics》1993,2(3):215-237
The paper addresses a part of the problem of classifying all 2-arc transitive graphs: namely, that of finding all groups acting 2-arc transitively on finite connected graphs such that there exists a minimal normal subgroup that is nonabelian and regular on vertices. A construction is given for such groups, together with the associated graphs, in terms of the following ingredients: a nonabelian simple group T, a permutation group P acting 2-transitively on a set , and a map F : Tsuch that x = x
–1 for all x
F() and such that Tis generated by F(). Conversely we show that all such groups and graphs arise in this way. Necessary and sufficient conditions are found for the construction to yield groups that are permutation equivalent in their action on the vertices of the associated graphs (which are consequently isomorphic). The different types of groups arising are discussed and various examples given. 相似文献
120.
L. I. Makarov 《Journal of Structural Chemistry》2005,46(4):738-743
Some questions emerged from electronic data processing of molecular structures (graphs) and its fragments have been considered in this work. Quantitative estimations of subgraph positions in molecular graphs are presented and some properties of their maximal common subgraphs are described. 相似文献