Browsing by Author "Chen, Zhen-Chun"

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Antimagicness of star forests
(2020-03-01)
Chen, Zhen-Chun
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Huang, Kuo-Ching
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Lin, Chiang
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Shang, Jen-Ling
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Lee, Ming-Ju
An edge labeling of a graph G is a bijection f : E(G) {1, 2, " " ", 1E(G)1}. The induced vertex sum f+ of f is a function defined on V(G) given by f+ (u) = E(G) f(uv) for all u E V(G). The value f+(u) is called the vertex sum at u. The graph G is called antimagic if there exists an edge labeling of G such that the vertex sums at all vertices of G are distinct. A star forest is the union of disjoint stars. Let S denote a star with n edges, and mS denote a star forest consisting of the disjoint m copies of S. It is known that mS2 is antimagic if and only if m = 1. In this study, a necessary condition and a sufficient condition are obtained whereby a star forest mS2 U Snr U Snz U " " " U Sn, (ni, n2, " " ", nk > 3) may be antimagic. In addition, a necessary and sufficient condition is obtained whereby a star forest mS2 US (n > 3) may be antimagic. Moreover, a graph consisting of disjoint stars together with an extra disjoint path is also verified to be antimagic.
Common multiples of paths and stars
(2019-07-01)
Chen, Zhen-Chun
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Shyu, Tay-Woei
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應用數學系
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Department of Applied Mathematics
A graph G is a common multiple of two graphs H-1 and H-2 if G is both H-1-decomposable and H-2-decomposable. In this paper, we consider the case where H-1 is the path of length k Pk+1 and H-2 is the star with 1 edges S-1. We determine, for all positive integers k and 1, the set of integers q for which there exists a common multiple of Pk+1 and S-1 having precisely q edges.
DECOMPOSING THE COMPLETE GRAPH INTO HAMILTONIAN PATHS (CYCLES) AND 3-STARS
(2020-01-01)
Lee, Hung-Chih
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Chen, Zhen-Chun
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應用數學系
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Department of Applied Mathematics
Let H be a graph. A decomposition of H is a set of edge-disjoint sub-graphs of H whose union is H. A Hamiltonian path (respectively, cycle) of H is a path (respectively, cycle) that contains every vertex of H exactly once. A k-star, denoted by S-k, is a star with k edges. In this paper, we give necessary and sufficient conditions for decomposing the complete graph into alpha copies of Hamiltonian path (cycle) and beta copies of S-3.
Pack Graphs with Subgraphs of Size Three
(2018-02-01)
Chen, Zhen-Chun
;
Fu, Hung-Lin
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Huang, Kuo-Ching
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應用數學系
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Department of Applied Mathematics
An H -packing F of a graph G is a set of edge -disjoint subgraphs of G in which each subgraph is isomorphic to H. The leave L or the remainder graph L of a packing F is the subgraph induced by the set of edges of G that does not occur in any subgraph of the packing F. If a leave L contains no edges, or simply L = Phi, then G is said to be H -decomposable, denoted by H broken vertical bar G. In this paper, we prove a conjecture made by Chartrand, Saba and Mynhardt [13]: If G is a graph of size q(G) 0 (mod 3) and delta(G) >= 2, then G is H -decomposable for some graph H of size 3.