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- Lenore Cowen, Wayne Goddard, C. Esther Jesurum
- Journal of Graph Theory
- 1997

A graph is (k, d)-colorable if one can color the vertices with k colors such that no vertex is adjacent to more than d vertices of its same color. In this paper we investigate the existence of suchâ€¦ (More)

A function Ï€ : V â†’ {1, . . . , k} is a broadcast coloring of order k if Ï€(u) = Ï€(v) implies that the distance between u and v is more than Ï€(u). The minimum order of a broadcast coloring is calledâ€¦ (More)

- Wayne Goddard, Teresa W. Haynes, Michael A. Henning, Lucas C. van der Merwe
- Discrete Mathematics
- 2004

A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G âˆ’ v is less than theâ€¦ (More)

- Lenore Cowen, Wayne Goddard, C. Esther Jesurum
- SODA
- 1997

An (ordinary vertex) coloring is a partition of the vertices of a graph into independent sets. The chromatic number is the minimum number of colors needed to produce such a partition. This paperâ€¦ (More)

- Lowell W. Beineke, Peter Hamburger, Wayne Goddard
- Discrete Mathematics
- 1994

A graph G is said to be packable by the graph F if its edges can be partitioned into copies of F. It is called randomly packable if what remains after deletion of the edges of a proper subgraph thatâ€¦ (More)

- Kunwarjit S. Bagga, Lowell W. Beineke, Wayne Goddard, Marc J. Lipman, Raymond E. Pippert
- Discrete Applied Mathematics
- 1992

Bagga, K.S., L.W. Beineke, W.D. Goddard, M.J. Discrete Applied Mathematics 37138 (1992) 13-28. Lipman and R.E. Pippert, A survey of integrity, A communication network can be considered to be highlyâ€¦ (More)

- Wayne Goddard
- Discrete Mathematics
- 2002

It is shown that in a 4-connected maximal planar graph there is for any four vertices a, b, c and d, a cycle in the graph that contains the four vertices and visits them in the order a, b, c and d.

- Odile Favaron, Gerd Fricke, +5 authors R. Duane Skaggs
- Discussiones Mathematicae Graph Theory
- 2004

A set S is an offensive alliance if for every vertex v in its boundary N(S)âˆ’S it holds that the majority of vertices in vâ€™s closed neighbourhood are in S. The offensive alliance number is the minimumâ€¦ (More)

- Wayne Goddard, Grzegorz Kubicki, Ortrud R. Oellermann, Songlin Tian
- J. Comb. Theory, Ser. B
- 1991

- Wayne Goddard
- Graphs and Combinatorics
- 2004

This paper generalises the concept of vertex pancyclic graphs. We define a graph as set-pancyclic if for every set S of vertices there is a cycle of every possible length containing S. We show thatâ€¦ (More)