Determination of all graphs whose eccentric graphs are clusters

Jin Akiyama, Takako Kodate, Kiyoko Matsunaga

Abstract


A disconnected graph G is called a cluster if G is not union of K2s (1-factor) but union of complete graphs of order at least two. J. Akiyama, K. Ando and D. Avis showed in Lemma 2.1 of [2] that G is equi-eccentric if the eccentric graph Ge is a cluster or pK2. And they also characterized all graphs whose eccentric graphs are complete graphs and pK2 in [2]. In this paper, we determined in Theorem 2 all graphs whose eccentric graphs are clusters, which is an extension of Lemma 2.1 in [2].

 

 


Keywords


eccentricity, eccentric graph, cluster, distance, radius

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DOI: http://dx.doi.org/10.5614/ejgta.2024.12.2.1

References

J. Akiyama, K. Ando, and D. Avis, Miscellaneous properties of equi-eccentric graphs, Ann. Discrete Math. 20 (1983), 13–23.

J. Akiyama, K. Ando, and D. Avis, Eccentric graphs, Discrete Mathematics. 56, No. 1 (1985), 1–6 .

D. Avis, The number of furthest neighbor pairs of a finite planar set, Amer. Math. Monthly 91 (1984), 417–420.

M. Behzad, G. Chartrand, and L. Lesniak-Foster, Graphs and Digraphs (Prindle, Weber & Schmidt, Reading. MA (1979).

F. Buckley, Self-centered graphs with given radius, Proc. 10th S. E. Conf. Comb., Graph Th., and Computing Congressus Numerantium XXIII, Utilitas Math., Winnipeg (1979), 211–215.

F. Harary, Graph Theory, Addison-Wesley, Reading, MA (1969).

K.R. Parthasarathy and R., Nandakumar, Unique eccentric point graphs, Discrete Math. 46 (1983), 69–74.

M. Shamos, Computational geometry, Ph.D. thesis, Yale University, New Haven. CT (1978).


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