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Sufficient conditions for triangle-free graphs to be super-$λ'$ | ||
| Transactions on Combinatorics | ||
| مقاله 3، دوره 7، شماره 3، آذر 2018، صفحه 29-36 اصل مقاله (228.44 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2018.106623.1523 | ||
| نویسندگان | ||
| Huiwen Cheng* 1؛ Yan-Jing Li2 | ||
| 1Department of Mathematics, Zhongguancun Institute | ||
| 2Department of Mathematics, Beijing Jiaotong University, China | ||
| چکیده | ||
| An edge-cut $F$ of a connected graph $G$ is called a restricted edge-cut if $G-F$ contains no isolated vertices. The minimum cardinality of all restricted edge-cuts is called the restricted edge-connectivity $λ'(G)$ of $G$. A graph $G$ is said to be $λ'$-optimal if $λ'(G)=\xi(G)$, where $\xi(G)$ is the minimum edge-degree of $G$. A graph is said to be super-$λ'$ if every minimum restricted edge-cut isolates an edge. In this paper, first, we provide a short proof of a previous theorem about the sufficient condition for $λ'$-optimality in triangle-free graphs, which was given in [J. Yuan and A. Liu, Sufficient conditions for $λ_k$-optimality in triangle-free graphs, Discrete Math., 310 (2010) 981--987]. Second, we generalize a known result about the sufficient condition for triangle-free graphs being super-$λ'$ which was given by Shang et al. in [L. Shang and H. P. Zhang, Sufficient conditions for graphs to be $λ'$-optimal and super-$λ'$, Network}, 309 (2009) 3336--3345]. | ||
| کلیدواژه‌ها | ||
| Triangle-free؛ restricted edge-cut؛ super-$ld'$ | ||
| مراجع | ||
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[1] A. Esfahanian, Genralized measures of fault tolerance with application to n -cub e networks, IEEE Tran. Comput. , 38 (1989) 1586{1591. [2] A. Esfahanian and S. Hakimi, On computing a conditional edge-connectivity of a graph, Inform. Process. Lett. , 27 (1988) 195{199. [3] A. Hellwig and L. Volkmannb, Sufficient conditions for ′ -optimality in graphs of diameter 2, Discrete Math. , 283 (2004) 113{204. [4] A. Hellwig and L. Volkmannb, Sufficient conditions for graphs to b e ′ -optimal, sup er-edge-connected and maximally edge-connected, J. Graph Theory , 48 (2005) 228{246. [5] L. Shang and H. P. Zhang, Sufficient conditions for graphs to b e ′ -optimal and sup er- ′ , Networks , 309 (2009) 3336{3345. [6] Y.-Q. Wang, Sup er restricted edge-connectivity of vertex-transitive graphs, Discrete Math. , 289 (2004) 199{205. [7] D. B. West, Introduction to Graph Theory , Prentice Hall Inc., Upp er Saddle River, NJ, 1996. [8] J. Yuan and A. Liu, Sufficient conditions for k -optimality in triangle-free grapsh, Discrete Math. , 310 (2010) 981{987. [9] J.-M. Xu and K.-L. Xu, On restricted edge-connectivity of graphs, Discrete Math. , 243 (2002) 291{298. | ||
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