Superconnectivity of graphs with odd girth g and even girth h

A maximally connected graph of minimum degree @d is said to be superconnected (for short super-@k) if all disconnecting sets of cardinality @d are the neighborhood of some vertex of degree @d. Sufficient conditions on the diameter to guarantee that a graph of odd girth g and even girth h>=g+3 is super-@k are stated. Also polarity graphs are shown to be super-@k.

[1]  Mehdi Behzad,et al.  Graphs and Digraphs , 1981, The Mathematical Gazette.

[2]  Miguel Angel Fiol,et al.  Maximally connected digraphs , 1989, J. Graph Theory.

[3]  Camino Balbuena,et al.  On the restricted connectivity and superconnectivity in graphs with given girth , 2007, Discret. Math..

[4]  Zoltán Füredi,et al.  Graphs without quadrilaterals , 1983, J. Comb. Theory, Ser. B.

[5]  Camino Balbuena,et al.  On the connectivity and superconnected graphs with small diameter , 2010, Discret. Appl. Math..

[6]  Ralph Tindell,et al.  Circulants and their connectivities , 1984, J. Graph Theory.

[7]  Frank Harary,et al.  Regular graphs with given girth pair , 1983, J. Graph Theory.

[8]  Camino Balbuena,et al.  Adjacency matrices of polarity graphs and of other C4-free graphs of large size , 2010, Des. Codes Cryptogr..

[9]  Makoto Imase,et al.  Connectivity of Regular Directed Graphs with Small Diameters , 1985, IEEE Transactions on Computers.

[10]  Angelika Hellwig,et al.  Maximally edge-connected and vertex-connected graphs and digraphs: A survey , 2008, Discret. Math..

[11]  F. Boesch.  Synthesis of reliable networks - a survey , 1986, IEEE Transactions on Reliability.

[12]  Paul Erdös,et al.  Graphs of diameter two with no 4-circuits , 1999, Discret. Math..

[13]  Zoltán Füredi,et al.  On the Number of Edges of Quadrilateral-Free Graphs , 1996, J. Comb. Theory, Ser. B.

[14]  Camino Balbuena,et al.  Connectivity of graphs with given girth pair , 2007, Discret. Math..

[15]  Mirka Miller,et al.  A lower bound on the order of regular graphs with given girth pair , 2007 .

[16]  G. Chartrand.  Graphs and Digraphs, Fourth Edition , 2004 .

[17]  Claudine Peyrat,et al.  Sufficient conditions for maximally connected dense graphs , 1987, Discret. Math..

[18]  Camino Balbuena,et al.  Superconnectivity of regular graphs with small diameter , 2009, Discret. Appl. Math..

[19]  Connie Maude Campbell.  On cages for girth pair (6, b) , 1997, Discret. Math..