A number theoretic problem on super line graphs

Bagga, Jay S.; Beineke, Lowell W.; Varma, Badri N.

doi:10.1016/j.akcej.2016.05.001

Cited by 4 publications

(4 citation statements)

References 2 publications

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“…In 2008, Li, Li, and Zhang [15] showed that if G has no isolated edges, then L 2 (G) is path-comprehensive, and that if G has at most one isolated edge, then L 2 (G) is vertex-pancyclic, answering a question posed by Bagga, Beineke, and Varma [14]. We refer to [16][17][18][19][20][21][22][23][24][25][26] for more results on super line graphs.…”

Section: Introductionmentioning

confidence: 99%

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On Several Parameters of Super Line Graph L2(G)

Meng

2023

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The super line graph of index r, denoted by Lr(G), is defined for any graph G with at least r edges. Its vertices are the sets of r edges of G, and two such sets are adjacent if an edge of one is adjacent to an edge of the other. In this paper, we give an explicit characterization for all graphs G with L2(G) being a complete graph. We present lower bounds for the clique number and chromatic number of L2(G) for several classes of graphs. In addition, bounds for the domination number of L2(G) are established in terms of the domination number of the line graph L(G) of a graph. A number of related problems on L2(G) are proposed for a further study.

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Section: Introductionmentioning

confidence: 99%

“…The line completion number lc(G) of a graph G is the least index r for which L r (G) is complete. This notion was investigated in [22][23][24][25][26]. For a graph G without an isolated vertex,…”

Section: Introductionmentioning

confidence: 99%

On Several Parameters of Super Line Graph L2(G)

Meng

2023

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“…Bagga et al [3][4][5][6][7][8] have done extensive work on the super line graphs. They discussed various properties of super line graphs in [3,4].…”

Section: Introductionmentioning

confidence: 99%

“…They determined the line completion numbers for various classes of graphs, viz., complete graph, path, cycle, fan, windmill, wheel, etc. Recently, they determined line completion number of complete bipartite graphs in [7]. Certain graphs are also characterized with the help of line completion number.…”

Section: Introductionmentioning

confidence: 99%

The line completion number of hypercubes

Tapadia

Waphare

2019

AKCE International Journal of Graphs and Combinatorics

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In 1992, Bagga, Beineke, and Varma introduced the concept of the super line graph of index r of a graph G, denoted by L r (G). The vertices of L r (G) are the r -subsets of E(G), and two vertices S and T are adjacent if there exist s ∈ S and t ∈ T such that s and t are adjacent edges in G. They also defined the line completion number l c (G) of graph G to be the minimum index r for which L r (G) is complete. They found the line completion number for certain classes of graphs. In this paper, we find the line completion number of hypercube Q n for every n. c

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Super Line Graphs and Super Line Digraphs

Beineke

Bagga

2021

Developments in Mathematics

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A number theoretic problem on super line graphs

Cited by 4 publications

References 2 publications

On Several Parameters of Super Line Graph L2(G)

On Several Parameters of Super Line Graph L2(G)

The line completion number of hypercubes

Super Line Graphs and Super Line Digraphs

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