ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 31 Mar 2023 11:52:16 GMT2023-03-31T11:52:16Z5081- The cordiality of one-point union of n copies of a graphhttps://scholarbank.nus.edu.sg/handle/10635/104272Title: The cordiality of one-point union of n copies of a graph
Authors: Shee, S.-C.; Ho, Y.-S.
Abstract: In this paper we give an equivalent definition of a cordial graph. The definition implies a previous result of Cahit (1986); it also enables us to find infinite families of noncordial graphs, derive some bound on the number of edges in a cordial graph and establish a necessary and sufficient condition for a one-point union of two n-cliques. Let G be a rooted graph. We denote by G(n) the graph obtained from n copies of G by identifying their roots. A sufficient condition for G(n) to be cordial is related to the solution of a system involving one equation and two inequalities with their coefficients depending on some binary labellings of G. According to the solvability of the system, we are able to establish a number of necessary and sufficient conditions for the cordiality of G(n) for certain classes of G, such as cycles, complete graphs, wheels, fans and flags. © 1993.
Thu, 01 Jul 1993 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1042721993-07-01T00:00:00Z
- The cordiality of the path-union of n copies of a graphhttps://scholarbank.nus.edu.sg/handle/10635/104273Title: The cordiality of the path-union of n copies of a graph
Authors: Shee, S.-C.; Ho, Y.-S.
Abstract: Let G1, G2,..., Gn be n (≥2) copies of a graph G. We denote by G (n) the graph obtained by adding an edge to Gi and Gi+1, i = 1, 2,..., n - 1, and we call G(n) the path-union of n copies of the graph G. We shall relate the cordiality of the path-union of n copies of a graph to the solution of a system involving an equation and two inequalities, and give some sufficient conditions for that path-union to be cordial. The path-unions of such graphs as cycles, wheels, fans, some cliques, Cartesian products and compositions of some graphs are shown to be cordial.
Fri, 10 May 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1042731996-05-10T00:00:00Z
- Graphs and Inverse Semigroupshttps://scholarbank.nus.edu.sg/handle/10635/103351Title: Graphs and Inverse Semigroups
Authors: Shee, S.C.; Teh, H.H.
Sat, 01 Jan 1983 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033511983-01-01T00:00:00Z
- On felicitous graphshttps://scholarbank.nus.edu.sg/handle/10635/103708Title: On felicitous graphs
Authors: Lee, S.-M.; Schmeichel, E.; Shee, S.C.
Abstract: A graph with n edges is called harmonious if it is possible to label the vertices with distinct numbers (modulo n) in such a way that the edge labels which are sums ofend-vertex labels are also distinct (modulo n). A generalization of harmonious graphs is felicitous graphs. In felicitous labelling distinct numbers (modulo n + 1) are used to label the vertices of a graph with n edges so that the edge labels are distinct (modulo n). We give some necessary conditions for a graph to be felicitous. Some families of graphs (cycles of order 4k, complete bipartite graphs, generalized Petersen graphs,...) are shown to be felicitous, while others (cycles of order 4k + 2, the complete graph Kitn when n≥5...) arenot. We also find that almost all graphs are not felicitous. © 1991.
Mon, 25 Nov 1991 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1037081991-11-25T00:00:00Z
- On skolem graceful graphshttps://scholarbank.nus.edu.sg/handle/10635/103756Title: On skolem graceful graphs
Authors: Lee, S.M.; Shee, S.C.
Abstract: A Skolem graceful labelling of graphs is introduced. It is shown that a tree is Skolem graceful iff it is graceful. The Skolem deficiency of a graph is defined and Skolem deficiencies of some well-known graphs are calculated. The class of Skolem graceful graphs is shown to be finite universal. © 1991.
Mon, 25 Nov 1991 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1037561991-11-25T00:00:00Z
- Some results on λ-valuation of graphs involving complete bipartite graphshttps://scholarbank.nus.edu.sg/handle/10635/104176Title: Some results on λ-valuation of graphs involving complete bipartite graphs
Authors: Shee, S.-C.
Abstract: In this paper we show that a graph G obtained from a complete bipartite graph Km,n and a collection of q (≤max\s{m,n\s}) stars Gi by joining the centre of G1 to every vertex of Km, n and joining the centre of Gi to a vertex (not the centre) of Gi+1 (i=1,2,...,q-1) is strongly harmonious. We also prove that a graph obtained from a collection of t complete bipartite graphs Kmi,ni with bipartition (Xi, Yi) by joining exactly one member in Yi with a member in Xi+1 (i=1,2,...,t-1) is strongly c-elegant. The windmill graph K(n) 2,2 of n complete bipartite graphs K2,2 with a common vertex is also shown to be harmonious for all n≥2. © 1991.
Sat, 19 Jan 1991 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1041761991-01-19T00:00:00Z
- Some extensions of a hypergraphhttps://scholarbank.nus.edu.sg/handle/10635/104159Title: Some extensions of a hypergraph
Authors: Shee, S.-C.
Abstract: It is shown how to construct a vertex-transitive hypergraph X* from a suitable collection of isomorphic copies of a given hypergraph X by identifying one or none of the vertices of every two copies in the collection. Moreover X* and X have the same strong chromatic number. If the hypergraph X is edge-coloured, then X* can be so constructed that it is strongly vertex-colour-transitive. This paper also considers the case where a section hypergraph or none of the vertices of every two isomorphic copies is identified in the construction of X*. © 1989 Springer-Verlag.
Fri, 01 Dec 1989 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1041591989-12-01T00:00:00Z
- H-extension of graphshttps://scholarbank.nus.edu.sg/handle/10635/103370Title: H-extension of graphs
Authors: Shee, S.C.; Teh, H.H.
Abstract: We consider the problem of constructing a graph G* from a collection of isomorphic copies of a graph G in such a way that for every two copies of G, either no vertices or a section graph isomorphic to a graph H is identified. It is shown that if G can be partitioned into vertex-disjoint copies of H, then G* can be made to have at most |H| orbits. A condition on G so that G* can be vertextransitive is also included. © 1984 Akadémiai Kiadó.
Fri, 01 Jun 1984 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033701984-06-01T00:00:00Z