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Median and quasi-median direct products of graphs

100%

Brešar B., Jha P., Klavžar S., Zmazek B.

Discussiones Mathematicae Graph Theory

2005

tom 25

nr 1-2

183-196

Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of G×P₃ is median if and only if G is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form G×K₂ are proved, and it is shown that the only nonbipartite quasi-median direct product is K₃×K₃.

The periphery graph of a median graph

100%

Brešar B., Changat M., Subhamathi A., Tepeh A.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 1

17-32

The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are path-like median graphs with arbitrarily large geodetic number. Peripheral expansion with respect to periphery graph is also considered, and connections with the concept of crossing graph are established.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Brešar B.

1 Changat M.

1 Jha P.

1 Klavžar S.

1 Subhamathi A.

1 Tepeh A.

1 Zmazek B.

1 2010

1 2005

Wyniki wyszukiwania

Median and quasi-median direct products of graphs

The periphery graph of a median graph