In this paper, we give infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [−1− √ 2,−2) and also infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [α1,−1− √ 2) where α1 is the smallest root(≈ −2.4812) of the polynomial x3 + 2x2 − 2x − 2. From these results, we ...

In the graph database literature the term “join” does not refer to an operator combining two graphs, but involves path traversal queries over a single graph. Current languages express binary joins through the combination of path traversal queries with graph creation operations. Such solution proves to be not efficient. In this paper we introduce a binary graph join operator and a corresponding ...

iv Acknowledgements v List of Tables vii List of Graphs vii

the energy of a graph is equal to the sum of the absolute values of its eigenvalues. two graphs of the same order are said to be equienergetic if their energies are equal. we point out the following two open problems for equienergetic graphs. (1) although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

We optimize multiway equijoins on relational tables using degree information. We give a new bound that uses degree information to more tightly bound the maximum output size of a query. On real data, our bound on the number of triangles in a social network can be up to 95 times tighter than existing worst case bounds. We show that using only a constant amount of degree information, we are able t...

This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset Ω̃. Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield...

for all x, y£L. It is easily shown that every join-endomorphism is an isotone correspondence (i.e. x^y implies ®x=i 8y). It is also easy to see that the set / of antecedents of 0 under any join-endomorphism is an ideal. (For these and other facts used in the sequel we refer to the textbook of G. Birkhoff, Lattice theory, rev. ed., New York, 1948, henceforth cited as LT.) G. Birkhoff states in L...

the edge tenacity te(g) of a graph g is dened as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...

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We consider the structure of Kr-free graphs with large minimum degree, and show that such graphs with minimum degree δ > (2r − 5)n/(2r − 3) are homomorphic to the join Kr−3 ∨ H where H is a triangle-free graph. In particular this allows us to generalize results from triangle-free graphs and show that Kr-free graphs with such minimum degree have chromatic number at most r+ 1. We also consider th...