On The Lattice of Trail Sets of a Connected Graph

Asha Saraswathi B; Lavanya S.

doi:https://doi.org/10.14445/22315373/IJMTT-V57P550

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 5 | Year 2018 | Article Id. IJMTT-V57P550 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P550

On The Lattice of Trail Sets of a Connected Graph

Asha Saraswathi B ,Lavanya S.

Citation :

Asha Saraswathi B ,Lavanya S., "On The Lattice of Trail Sets of a Connected Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 5, pp. 366-367, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P550

Abstract

In this paper Trail set is defined for a finite connected graph G and it is found that the set of all trail sets ȶ(G) together with empty set partially ordered by set inclusion relation forms a lattice. Also derived graph of G, denoted by Gd is defined such that lattices ȶ(G) and ȶ(Gd) are isomorphic. Some of the properties of the lattices so obtained are studied. The definition of trail sets is extended to directed graphs and studied.

Keywords

connected graph, lattice, tree, pendant vertex, Connected digraph, Path, Circuit.

References

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