%0 Journal Article
%T Signed graphs connected with the root lattice
%A RN Yadav
%J BIBECHANA
%P 157-160
%@ 2382-5340
%D 2014
%R 10.3126/bibechana.v11i0.10396
%X For any base of the root lattice (An) we can construct a signed graph. A signed graph is one whose edges are signed by +1 or -1. A signed graph is balanced if and only if its vertex set can be divided into two sets-either of which may be empty¨Cso that each edge between the sets is negative and each edge within a set is positive. For a given signed graph Tsaranov, Siedel and Cameron constructed the corresponding root lattice. In the present work we have dealt with signed graphs corresponding to the root lattice An. A connected graph is called a Fushimi tree if its all blocks are complete subgraphs. A Fushimi tree is said to be simple when by deleting any cut vertex we have always two connected components. A signed Fushimi tree is called a Fushimi tree with standard sign if it can be transformed into a signed Fushimi tree whose all edges are signed by +1 by switching. Here we have proved that any signed graph corresponding to An is a simple Fushimi tree with standard sign. Our main result is that s simple Fushimi tree with standard sign is contained in the cluster given by a line.
%K Signed graph
%K Root lattice
%K Fushimi tree
%U http://www.nepjol.info/index.php/BIBECHANA/article/view/10396