Sufficient conditions for locally connected graphs
Sufficient conditions for planar graphs to be 2-distance ()-colourable.
Sufficient conditions for the minimum 2-distance colorability of plane graphs of girth 6.
Sufficient conditions on the existence of factors in graphs involving minimum degree
For a set of graphs, an -factor of a graph is a spanning subgraph of , where each component of is contained in . It is very interesting to investigate the existence of factors in a graph with given minimum degree from the prospective of eigenvalues. We first propose a tight sufficient condition in terms of the -spectral radius for a graph involving minimum degree to contain a star factor. Moreover, we also present tight sufficient conditions based on the -spectral radius and the distance...
Suites infinies à répétitions bornées.
Sulla famiglia dei flocks lineari di una quadrica iperbolica assolutamente irriducibile di uno spazio proiettivo finito
In questa Nota diamo una caratterizzazione dell'insieme di tutti i flocks lineari della quadrica iperbolica assolutamente irriducibile in .
Sum labellings of cycle hypergraphs
A hypergraph is a sum hypergraph iff there are a finite S ⊆ IN⁺ and d̲, [d̅] ∈ IN⁺ with 1 < d̲ ≤ [d̅] such that is isomorphic to the hypergraph where V = S and . For an arbitrary hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices such that is a sum hypergraph. Generalizing the graph Cₙ we obtain d-uniform hypergraphs where any d consecutive vertices of Cₙ form an edge. We determine sum numbers and investigate properties of sum labellings for this...
Sum list coloring arrays.
Sum List Edge Colorings of Graphs
Let G = (V,E) be a simple graph and for every edge e ∈ E let L(e) be a set (list) of available colors. The graph G is called L-edge colorable if there is a proper edge coloring c of G with c(e) ∈ L(e) for all e ∈ E. A function f : E → ℕ is called an edge choice function of G and G is said to be f-edge choosable if G is L-edge colorable for every list assignment L with |L(e)| = f(e) for all e ∈ E. Set size(f) = ∑e∈E f(e) and define the sum choice index χ′sc(G) as the minimum of size(f) over all edge...
Sum of squares of degrees in a graph.
Sum relations for Lucas sequences.
Summaries of articles published in this issue
Sums involving moments of reciprocals of binomial coefficients.
Sums involving the inverses of binomial coefficients.
Sums of Powered Characteristic Roots Count Distance-Independent Circular Sets
Significant values of a combinatorial count need not fit the recurrence for the count. Consequently, initial values of the count can much outnumber those for the recurrence. So is the case of the count, Gl(n), of distance-l independent sets on the cycle Cn, studied by Comtet for l ≥ 0 and n ≥ 1 [sic]. We prove that values of Gl(n) are nth power sums of the characteristic roots of the corresponding recurrence unless 2 ≤ n ≤ l. Lucas numbers L(n) are thus generalized since L(n) is the count in question...
Sums of reciprocals of the central binomial coefficients.
Sums of sets of group elements
Sunflowers in lattices.
Super boson-fermion correspondence
We establish a super boson-fermion correspondence, generalizing the classical boson-fermion correspondence in 2-dimensional quantum field theory. A new feature of the theory is the essential non-commutativity of bosonic fields. The superbosonic fields obtained by the super bosonization procedure from super fermionic fields form the affine superalgebra . The converse, super fermionization procedure, requires introduction of the super vertex operators. As applications, we give vertex operator constructions...
Super mean number of a graph