On felicitous graphs

Lee, Sin-Min; Schmeichel, E. F.; Shee, S. C.

doi:10.1016/0012-365x(91)90256-2

Cited by 22 publications

(20 citation statements)

References 3 publications

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“…Lee, Schmeichel, and Shee [55] have proved that the generalized Petersen graph P(n, k) is harmonious for all odd n and all k. The harmonious case where n is even and the gracefulness of P(n, k) appear to be uninvestigated. Several well-known isolated graphs have been examined.…”

Section: Mlscellaneous Resultsmentioning

confidence: 99%

A survey: Recent results, conjectures, and open problems in labeling graphs

Gallian

1989

Journal of Graph Theory

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Section: Mlscellaneous Resultsmentioning

confidence: 99%

A survey: Recent results, conjectures, and open problems in labeling graphs

Gallian

1989

Journal of Graph Theory

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“…For example, C 6 is bipartite, but it has no odd -edge labeling. In [6], it has been proved that P 2 C 2k+1 and P 3 C 2k+1 are felicitous and conjectured that P n C 2k+1 is felicitous for all n4. But P 5 C 5…”

Section: Called An Odd Edge Under F If F*(e) Is Odd For Any Two Gramentioning

confidence: 99%

“…Several graph labelings have been found in Gallian Survey [4]. Lee, Schmeichel and Shee [6] introduced the concept of felicitous graph as a generalization of a harmonious graph. A felicitous labeling of a graph G, with q edges is an injection f:V(G) → {0, 1, 2,. .…”

Section: Introductionmentioning

confidence: 99%

On Near Felicitous Labelings of Graphs

Gomathi¹,

Nagarajan²,

Nellaimurugan³

2013

International Journal of Mathematics and Soft Computing

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A simple graph G is called near felicitous if there exists a 1 -1 function f:V(G) → {0, 1, 2, . .. , q -1, q + 1} such that the set of induced edge labels f *(uv) = (f(u) + f(v)) (mod q) are all distinct when the addition is taken modulo q with residues 1, 2, 3, . . . , q. It is shown that an even subgraph of a near felicitous graph with an even number of edges contain an even number of odd labeled edges. As a consequence, some families of graphs are shown to be non -near felicitous.

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“…Lee et al [12] introduced the definition of felicitous graphs as a generalization of the definition of harmonious graphs. A graph G of size q is called felicitous if there exists an injective function f : V (G) → Z q+1 such that when each uv ∈ E (G) is labeled f (u) + f (v) (mod q), the resulting edge labels are distinct.…”

Section: Introductionmentioning

confidence: 99%

On Partitional and Other Related Graphs

Ichishima

Oshima

2011

Math.Comput.Sci.

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The partitional graphs, which are a subclass of the sequential graphs, were recently introduced by Ichishima and Oshima (Math Comput Sci 3:39-45, 2010), and the cartesian product of a partitional graph and K 2 was shown to be partitional, sequential, harmonious and felicitous. In this paper, we present some necessary conditions for a graph to be partitional. By means of these, we study the partitional properties of certain classes of graphs. In particular, we completely characterize the classes of the graphs B m and K m,2 × Q n that are partitional. We also establish the relationships between partitional graphs and graphs with strong α-valuations as well as strongly felicitous graphs.

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On felicitous graphs

Cited by 22 publications

References 3 publications

A survey: Recent results, conjectures, and open problems in labeling graphs

A survey: Recent results, conjectures, and open problems in labeling graphs

On Near Felicitous Labelings of Graphs

On Partitional and Other Related Graphs

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