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Paths and cycles of hypergraphs
Science in China Series A: Mathematics, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jianfang Wang, Tony T. Lee
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Journal of Graph Theory, 1978
AbstractLet k be a positive integer, and S a nonempty set of positive integers. Suppose that G is a connected graph containing a path of length k, and that each path P of length k in G is contained in some cycle C(P) of length s ∈ S. We prove that every path of length less than k can be extended to a path of length k in G.
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AbstractLet k be a positive integer, and S a nonempty set of positive integers. Suppose that G is a connected graph containing a path of length k, and that each path P of length k in G is contained in some cycle C(P) of length s ∈ S. We prove that every path of length less than k can be extended to a path of length k in G.
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On the observability of path and cycle graphs
49th IEEE Conference on Decision and Control (CDC), 2010In this paper we investigate the observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. More in detail, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the
PARLANGELI, GIANFRANCO +1 more
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, 1997 A walk in a graph G is a finite sequence of vertices x 0, x 1, ..., x n and edges a 1, a 2, ..., a n of G: $${x_0},{a_1},{x_1},{a_2}, \ldots ,{a_n},{x_n},$$ where the endpoints of a i are x i−1 and x i for each i. A simple walk is a walk in which no edge is repeated.
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Journal of Graph Theory, 2011
AbstractIn 1960 Ore proved the following theorem: Let G be a graph of order n. If d(u) + d(v)≥n for every pair of nonadjacent vertices u and v, then G is hamiltonian. Since then for several other graph properties similar sufficient degree conditions have been obtained, so‐called “Ore‐type degree conditions”. In [R. J. Faudree, R. H. Schelp, A.
Arnfried Kemnitz +3 more
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AbstractIn 1960 Ore proved the following theorem: Let G be a graph of order n. If d(u) + d(v)≥n for every pair of nonadjacent vertices u and v, then G is hamiltonian. Since then for several other graph properties similar sufficient degree conditions have been obtained, so‐called “Ore‐type degree conditions”. In [R. J. Faudree, R. H. Schelp, A.
Arnfried Kemnitz +3 more
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Estrada index of cycles and paths
Chemical Physics Letters, 2007It was shown that the recently introduced Estrada index is remarkably well approximated by a linear funcion in n where n stands for the number of vertices in molecular graph.
Ante Graovac, Ivan Gutman
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Modularity of cycles and paths in graphs
Journal of the ACM, 1991Certain problems related to the length of cycles and paths modulo a given integer are studied. Linear-time algorithms are presented that determine whether all cycles in an undirected graph are of length P mod Q and whether all paths between two specified nodes are of length P
E. M. Arkin +2 more
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Hamilton Cycles and Paths in Fullerenes
Journal of Chemical Information and Modeling, 2007AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.
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2013
By default, each path is timed for a single cycle, i.e., data launched at any edge of the clock should be captured by the next flop at the next rising edge of the clock on the destination flop. Figure 12.1 shows this relationship.
Sridhar Gangadharan, Sanjay Churiwala
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By default, each path is timed for a single cycle, i.e., data launched at any edge of the clock should be captured by the next flop at the next rising edge of the clock on the destination flop. Figure 12.1 shows this relationship.
Sridhar Gangadharan, Sanjay Churiwala
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