A new like quantity based on “Estrada index”.
A new lower bound for the inducibility of a graph
A new lower bound on the density of vertex identifying codes for the infinite hexagonal grid.
A New Method for Computing the Eccentric Connectivity Index of Fullerenes
ACM Computing Classification System (1998): G.2.2, G.2.3.The eccentric connectivity index of the molecular graph G, ξ^c (G), was proposed by Sharma, Goswami and Madan. It is defined as ξ^c (G) = Σu∈V(G)degG(u) ecc(u), where degG(x) denotes the degree of the vertex x in G and ecc(u) = Max{d(x, u) | x ∈ V (G)}. In this paper this graph invariant is computed for an infinite class of fullerenes by means of group action.
A New Necessary Condition for the Vertex Visibility Graphs of Simple Polygons.
A new proof of a characterization of the set of all geodesics in a connected graph
A new proof of a theorem of Dirac on the number of edges in critical graphs.
A new proof of the four-colour theorem.
A New Proof of the Szeged-Wiener Theorem
A New Proof that 4-Connected Planar Graphs are Hamiltonian-Connected
We prove a theorem guaranteeing special paths of faces in 2-connected plane graphs. As a corollary, we obtain a new proof of Thomassen’s theorem that every 4-connected planar graph is Hamiltonian-connected.
A new spectral method for determining the number of spanning trees.
A new upper bound for the chromatic number of a graph
Let G be a graph of order n with clique number ω(G), chromatic number χ(G) and independence number α(G). We show that χ(G) ≤ [(n+ω+1-α)/2]. Moreover, χ(G) ≤ [(n+ω-α)/2], if either ω + α = n + 1 and G is not a split graph or α + ω = n - 1 and G contains no induced .
A new upper bound for the Laplacian spectral radius of a graph.
A new upper bound on the total domination number of a graph.
A non graph theory approach to Ulam's conjecture
A non-differentiablity result for the inversion operator between Sobolev spaces.
A not on dominating set with Maple.
A Note on a Bermond's Conjecture
A Note on a Broken-Cycle Theorem for Hypergraphs
Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there
A note on a conjecture on niche hypergraphs
For a digraph , the niche hypergraph of is the hypergraph having the same set of vertices as and the set of hyperedges and there exists a vertex such that or . A digraph is said to be acyclic if it has no directed cycle as a subdigraph. For a given hypergraph , the niche number is the smallest integer such that together with isolated vertices is the niche hypergraph of an acyclic digraph. C. Garske, M. Sonntag and H. M. Teichert (2016) conjectured that for a linear hypercycle...