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Almost Self-Centered Graphs 被引量：3

Almost Self-Centered Graphs
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摘要 The center of a graph is the set of vertices with minimum eccentricity. Graphs in which all vertices are central are called self-centered graphs. In this paper almost self-centered （ASC） graphs are introduced as the graphs with exactly two non-central vertices. The block structure of these graphs is described and constructions for generating such graphs are proposed. Embeddings of arbitrary graphs into ASC graphs are studied. In particular it is shown that any graph can be embedded into an ASC graph of prescribed radius. Embeddings into ASC graphs of radius two are studied in more detail. ASC index of a graph G is introduced as the smallest number of vertices needed to add to G such that G is an induced subgraph of an ASC graph. The center of a graph is the set of vertices with minimum eccentricity. Graphs in which all vertices are central are called self-centered graphs. In this paper almost self-centered （ASC） graphs are introduced as the graphs with exactly two non-central vertices. The block structure of these graphs is described and constructions for generating such graphs are proposed. Embeddings of arbitrary graphs into ASC graphs are studied. In particular it is shown that any graph can be embedded into an ASC graph of prescribed radius. Embeddings into ASC graphs of radius two are studied in more detail. ASC index of a graph G is introduced as the smallest number of vertices needed to add to G such that G is an induced subgraph of an ASC graph.
作者 Sandi KLAVZAR Kishori P. NARAYANKAR H. B. WALIKAR
机构地区 Faculty of Mathematics and Physics Faculty of Natural Sciences and Mathematics Department of Computer Science
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第12期2343-2350,共8页 数学学报（英文版）
关键词 RADIUS diameter self-centered graph almost self-centered graph Radius, diameter, self-centered graph, almost self-centered graph
分类号 TP391.41 [自动化与计算机技术—计算机应用技术] TN943.6 [电子电信—信号与信息处理]
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参考文献16

  • 1Akiyama, J., Ando, J. K., Avis, D.: Miscellaneous Properties of Equi-Eccentric Graphs. In: Convexity and graph theory (Jerusalem, 1981), North-Holland Math. Stud. 87, 13-23, North-Holland, Amsterdam, 1984.
  • 2Buckley, F., Miller, Z., Slater, P. J.: On graphs containing a given graph as center. J. Graph Theory, 5, 427 434 (1981).
  • 3Janakiraman, T. N.: On self-centered graphs. J. Ramanujan Math. Soc., T, 83-92 (1992).
  • 4Negami, S., Xu, G. H.: Locally geodesic cycles in 2-self-centered graphs. Discrete Math., 58,263-268 (1986).
  • 5Buckley, F.: Self-centered graphs. Ann. New York Acad. Sci., 576, 71-78 (1989).
  • 6Lee, S.-M., Wang, P.-C.: On groups of automorphisms of self-centered graphs. Bull. Math. Soc. Sci. Math. Roumanie (g. S.), 34(82), 311-316 (1990).
  • 7Janakiraman, T. N., Bhanumathi, M., Muthammai, S.: Self-centered super graph of a graph and center number of a graph. Ars Combin., 87, 271-290 (2008).
  • 8Chartrand, G., Gu, W., Schultz, M., et al.: Eccentric graphs. Networks, 34, 115-121 (1999).
  • 9Gimbert, J., L6pez, N., Miller, M., et al.: Characterization of eccentric digraphs. Discrete Math., 306, 210-219 (2006).
  • 10Walikar, H. B., Narayankar, K. P.: Almost self-centered ASC(R)-graphs. Submitted.

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Acta Mathematica Sinica,English Series
2011年 第12期

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