It is known that bipartite distance-regular graphs with diameter D > 3, valency k > 3, intersection number c2 > 2 and eigenvalues k = θ0 > θ1 > · · · > θD satisfy θ1 6 k− 2 and thus θD−1 > 2− k. In this paper we classify non-complete distanceregular graphs with valency k > 2, intersection number c2 > 2 and an eigenvalue θ satisfying −k < θ 6 2 − k. Moreover, we give a lower bound for valency k ...

Current paper presents a new technique for static compaction of sequential circuit tests that are divided into independent test sequences. The technique implements effective representation of fault matrices by weighted bipartite graphs. The approach contains a preprocessing step for determining the set of essential vectors. Subsequently, implications and a greedy search algorithm is applied. Th...

Geometric versions of Ramsey-type and Turán-type problems are studied in a special but natural representation of bipartite graphs and similar questions are asked for general representations. A bipartite geometric graphG(m,n) = [A,B] is simple if the vertex classes A,B of G(m,n) are represented in R2 as A = {(1, 0), (2, 0), . . . , (m, 0)}, B = {(1, 1), (2, 1), . . . , (n, 1)} and the edge ab is...

ABSTRACT Let ‎G=(V,E) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎V‎‎‎ ‎and ‎edge ‎set ‎‎‎E. ‎The Szeged index ‎of ‎‎G is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎G ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎If ‎‎‎‎S ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎V ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎S ‎of ‎size ‎3. ‎Then ‎we ‎define ‎t...

We present the tables of feasible parameters primitive 3 -class Q -polynomial association schemes and 4 - 5 -bipartite (on up to 2800 , 10000 50000 vertices, respectively), accompanied by a number nonexistence results for such obtained analysing triple intersection numbers putative open cases.

In this paper, we propose a novel compact representation called weighted bipartite hypergraph to exploit the fertility model, which plays a critical role in word alignment. However, estimating the probabilities of rules extracted from hypergraphs is an NP-complete problem, which is computationally infeasible. Therefore, we propose a divide-and-conquer strategy by decomposing a hypergraph into a...

We investigate which chordal graphs have a representation as intersection graphs of pseudosegments. The main contribution is a construction which shows that all chordal graphs which have a representation as intersection graph of subpaths on a tree are representable. A family of intersection graphs of substars of a star is used to show that not all chordal graphs are representable by pseudosegme...

As a general case of molecular graphs of benzenoid hydrocarbons, we study plane bipartite graphs with Kekulé structures (1-factors). A bipartite graph G is called elementary if G is connected and every edge belongs to a 1-factor of G. Some properties of the minimal and the maximal 1-factor of a plane elementary graph are given. A peripheral face f of a plane elementary graph is reducible, if th...

The class of Bipartite Distance Hereditary (BDH) graphs is the intersection between bipartite domino-free and chordal bipartite graphs. Graphs in both the latter classes have linearly many maximal bicliques, implying the existence of polynomial-time algorithms for computing the associated Galois lattice. Such a lattice can indeed be built in O(m×n) worst case-time for a domino-free graph with m...

Let Γ denote a bipartite distance-regular graph with diameter D. In [J. S. Caughman, Bipartite Q-polynomial distance-regular graphs, Graphs Combin. 20 (2004), 47–57], Caughman showed that if D > 12, then Γ is Q-polynomial if and only if one of the following (i)-(iv) holds: (i) Γ is the ordinary 2D-cycle, (ii) Γ is the Hamming cube H(D, 2), (iii) Γ is the antipodal quotient of the Hamming cube H...