Some Properties of the Lattice of Path Sets of a Connected Graph
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DOI:
https://doi.org/10.14419/ijet.v7i4.10.20919Keywords:
Connected graph, block, cut point.Abstract
It is known that the set of all path sets of a finite connected graph G together with empty set partially ordered by set inclusion relation forms a lattice denoted by PATH(G). In this paper we studied some properties of PATH(G). In fact, it has been shown that an element of PATH(G) is doubly irreducible if and only if it contains a single vertex which is not a cut vertex of G. Also it is proved that PATH(G) is planar if and only if G is a chain of three or more blocks.
References
Asha saraswathi B and Lavanya S, “On the lattice of convex edge sets of a connected directed graph”, International journal of pure and applied mathematical sciences Volume 8, Number 2(2015), pp155-161
Birkhoof.G. “Lattice theory”, American mathematical Soc, Third edition(New York, 1967)
D Kelly and I Rival, “planar lattices”, canad j math, 27 no 3(1975),635-665.
Gratzer, G: “General lattice theory”, Birkhauser Verlag, academic press,1978
Harary F: “Graph theory”, Addision-wesley, 1969
View more references (7)
Harary F,etl. “Boolean distance for graphs”, Discrete mathematics. 39(1982)123-127
Girishkumara R and Lavanya S, “On the lattice of convex sets and path sets of a connected graph”, International Journal of Mathemat-ics Research. Volume 7,number 2(2015), pp 197-202
Lavanya.S and Subramanya Bhat.S, “On the lattice of convex sets of Connected graph”, Global journal of pure and applied Mathemat-ics. Vol 7, 2(2011), 157-162
Lavanya .S, “On the lattice of path sets of a connected graph”, In-dian Journal of Mathematics research, Vol 1, Nov 1(2013), 219-222
Pfaltz.J.L.,“Convexity in directed graphs”, J.Combinatorical theory. 10(1971), 143-162
Sergio R Canoy,Jr and I.J.LGraces, “Convex sets under some graph operations”, Graphs and combinotorics. (2002)18,787-79.
Sachs .D. The lattice of sub algebras of a Boolean algebra, Canada. J.Math.14 (1962), 451-460.