On pathos lict subdivision of a tree

Let G be a graph and [E.sub.1] C E(G). A Smarandachely [E.sub.1]-lict graph [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (G) of a graph G is the graph whose point set is the union of the set of lines in [E.sub.1] and the set of cutpoints of G in which two points are adjacent if and only if th...

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Bibliographic Details
Published in:International journal of mathematical combinatorics 2010-12, Vol.4, p.100
Main Authors: Mirajkar, Keerthi G, Kadakol, Iramma M
Format: Article
Language:English
Subjects:
Combinatorics
Graphs
Mathematics
Number theory
Trees (Graph theory)
Online Access:Get full text
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Summary:Let G be a graph and [E.sub.1] C E(G). A Smarandachely [E.sub.1]-lict graph [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (G) of a graph G is the graph whose point set is the union of the set of lines in [E.sub.1] and the set of cutpoints of G in which two points are adjacent if and only if the corresponding lines of G are adjacent or the corresponding members of G are incident.Here the lines and cutpoints of G are member of G. Particularly, if [E.sub.1] = E(G), a Smarandachely E(G)-lict graph [n.sup.E(G)](G) is abbreviated to lict graph of G and denoted by n(G). In this paper, the concept of pathos lict sub-division graph [P.sub.n][S(T)] is introduced. Its study is concentrated only on trees. We present a characterization of those graphs, whose lict sub-division graph is planar, outerplanar, maximal outerplanar and minimally nonouterplanar. Further, we also establish the characterization for [P.sub.n][S(T)] to be eulerian and hamiltonian. Key Words: pathos, path number, Smarandachely lict graph, lict graph, pathos lict sub-division graphs, Smarandache path k-cover, pathos point. AMS(20 10): 05C10, 05C99
ISSN:1937-1055
1937-1047