Estimation of the index of
Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix.
Estrada index of iterated line graphs
Eternal Domination: Criticality and Reachability
We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached. The study of the stronger assertion that such a set can be reached after a single attack is defended leads to the study of graphs which are critical in the sense that deleting any vertex reduces the eternal domination number. Examples of these graphs and tight...
Etude du spectre pour certains noyaux sur un arbre
Etude sur les plans en blocs incomplets equilibres
Eulerian polar graphs
Euler's idoneal numbers and an inequality concerning minimal graphs with a prescribed number of spanning trees
Let be the least number for which there exists a simple graph with vertices having precisely spanning trees. Similarly, define as the least number for which there exists a simple graph with edges having precisely spanning trees. As an -cycle has exactly spanning trees, it follows that . In this paper, we show that and if and only if , which is a subset of Euler’s idoneal numbers. Moreover, if and we show that and This improves some previously estabilished bounds.
Evaluating a weighted graph polynomial for graphs of bounded tree-width.
Even [a,b]-factors in graphs
Let a and b be integers 4 ≤ a ≤ b. We give simple, sufficient conditions for graphs to contain an even [a,b]-factor. The conditions are on the order and on the minimum degree, or on the edge-connectivity of the graph.
Even and odd tournament matrices with minimum rank over finite fields.
Even bonds of prescribed directed parity.
Even circuits of prescribed clockwise parity.
Even factor of bridgeless graphs containing two specified edges
An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Let be a bridgeless simple graph with minimum degree at least . Jackson and Yoshimoto (2007) showed that has an even factor containing two arbitrary prescribed edges. They also proved that has an even factor in which each component has order at least four. Moreover, Xiong, Lu and Han (2009) showed that for each pair of edges and of , there is an even factor containing and in which each...
Every connected acyclic digraph of height 1 is neighbourhood-realizable
Every finite lattice can be embedded in the lattice of all equivalences over a finite set (Preliminary communication)
Every forest can be obtained from a minimal block.
Every graph is an induced isopart of a circulant
Evolution in random environment and structural instability.
Evolutionary families of sets.