ENERGY OF COMPLEMENT OF STARS

pdf abstract DOI : http://dx.doi.org/10.22342/jims.19.1.125.15-2

Designs associated with maximum independent sets of a graph

A (v, beta (o) , mu)-design over regular graph G = (V, E) of degree d is an ordered pair D = (V, B), where |V| = v and B is the set of maximum independent sets of G called blocks such that if i, j a V, i not equal j and if i and j are not adjacent in G then there are exactly mu blocks containing i and j. In this paper, we study (v, beta (o) , mu)-designs over the graphs K (n) x K (n) , T(n)-triangular graphs, L (2)(n)-square lattice graphs, Petersen graph, Shrikhande graph, Clebsch graph and the Schlafli graph and non-existence of (v, beta (o) , mu)-designs over the three Chang graphs T (1)(8), T (2)(8) and T (3)(8)

No Huckel graph is hyperenergetic

If G is a molecular graph with n vertices and if l1, l2, ..., ln are its eigenvalues, then the energy of G is equal to E(G) = |l1| + |l2|+ ... + |ln|. If E(G) > 2n 2, then G is said to be hyperenergetic. We show that no Hückel graph (= the graph representation of a conjugated hydrocarbon within the Hückel molecular orbital model) is hyperenergetic