članak: 1 od 1  
Applicable Analysis and Discrete Mathematics
2008, vol. 2, br. 1, str. 114-117
jezik rada: engleski
neklasifikovan
doi:10.2298/AADM0801114P

A note on signed degree sets in signed bipartite graphs
(naslov ne postoji na srpskom)
University of Kashmir, Department of Mathematics, Srinagar, India

e-adresa: sdpirzada@yahoo.co.in

Sažetak

(ne postoji na srpskom)
A signed bipartite graph G(U, V) is a bipartite graph in which each edge is assigned a positive or a negative sign. The signed degree of a vertex x in G(U, V) is the number of positive edges incident with x less the number of negative edges incident with x. The set S of distinct signed degrees of the vertices of G(U, V) is called its signed degree set. In this paper, we prove that every set of integers is the signed degree set of some connected signed bipartite graph.

Ključne reči

signed graph; signed bipartite graph; signed degree; signed degree set

Reference

Chartrand, G., Gavlas, H., Harary, F., Schultz, M. (1994) On signed degrees in signed graphs. Czechoslovak Mathematical J., 44, 677-690
Hakimi, S.L. (1962) On the realizability of a set of integers as degrees of the vertices of a graph. SIAM J. Appl. Math, 10, 496-506
Harary, F. (1953) On the notion of balance in a signed graph. Michigan Math. J., 2, 143-146
Kapoor, S.F., Polimeni, A.O., Wall, C.E. (1977) Degree sets for graphs. Fund. Math, 65, 189-194
Pirzada, S., Naikoo, T.A., Dar, F.A. (2007) Degree sets in bipartite and 3-partite graphs. Oriental J. of Mathematical Sciences, 1, 47-53
Pirzada, S., Naikoo, T.A., Dar, F.A. (2007) Signed degree sets in signed graphs. Czech. Math. J., 57, 132, 843-848
Yan, J.H., Lih, K.W., Kuo, D., Chang, G.J. (1997) Signed degree sequences of signed graphs. J Graph Theory, 26 111-117