On Harmonious Labelings of the Balanced Quintuple Shells

Xi Yue

doi:10.1007/978-3-642-24097-3_32

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On Harmonious Labelings of the Balanced Quintuple Shells

https://doi.org/10.1007/978-3-642-24097-3_32

On Harmonious Labelings of the Balanced Quintuple Shells

Jan 1, 2011
Xi Yue

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Abstract

Abstract A multiple shell MS {n1t1, n2t2 ,. . . , nrtr } is a graph formed by ti shells of widths n i , 1 ≤ i ≤ r, which have a common apex. This graph has \(\sum^{r}_{i=1}\) ti(ni–1)+1 vertices. A multiple shell is said to be balanced with width w if it is of the form MS{ws} or MS{(w + 1)t, ws}. Deb and Limaye have conjectured that all multiple shells are harmonious. The conjecture has been shown true for the balanced double shells, the balanced triple shells and the balanced quadruple shells. In this paper, the conjecture is proved to be true for the balanced quintuple shells.Keywordsharmonious graphmultiple shellvertex labelingedge labeling

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Graceful Labeling of Bow Graphs and Shell-Flower Graphs

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INTERNATIONAL JOURNAL OF COMPUTING ALGORITHM
Jeba Jesintha J

A graceful labeling of a graph G with ‘q’ edges and vertex set V is an injection f: VG → {0,1,2,….q} with the property that the resulting edge labels are also distinct, where an edge incident with vertices u and v is assigned the label |fu – fv| . A graph which admits a graceful labeling is called a graceful graph. A Shell graph is defined as a cycle Cnwith n -3 chords sharing a common end point called the apex . Shell graphs are denoted as Cn, n- 3. A multiple shell is defined to be a collection of edge disjoint shells that have their apex in common. Hence a double shell consists of two edge disjoint shells with a common apex.