Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix.
Etude du spectre pour certains noyaux sur un arbre
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.
Every forest can be obtained from a minimal block.
Exactly solvable and unsolvable shortest network problems in 3D-space.
Existence of -factors in powers of connected graphs
Extended trees of graphs
An extended tree of a graph is a certain analogue of spanning tree. It is defined by means of vertex splitting. The properties of these trees are studied, mainly for complete graphs.
Extremal algebraic connectivities of certain caterpillar classes and symmetric caterpillars.
Extremal Matching Energy of Complements of Trees
Gutman and Wagner proposed the concept of the matching energy which is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. And they pointed out that the chemical applications of matching energy go back to the 1970s. Let T be a tree with n vertices. In this paper, we characterize the trees whose complements have the maximal, second-maximal and minimal matching energy. Furthermore, we determine the trees with edge-independence number p whose complements have...
Extremely Irregular Graphs
Factorization of the Green's operator and weak-type estimates for a random walk on a tree.
Finding a spanning tree of a graph with maximal number of terminal vertices
Finding Minimal Branchings With a Given Number of Arcs
Fixed point theorems in CAT(0) spaces and -trees.
Forest decompositions of graphs with cyclomatic number 2.
Forest decompositions of graphs with cyclomatic number 3.
From paths to stars.
Front-divisors of trees.
Functions on adjacent vertex degrees of trees with given degree sequence
In this note we consider a discrete symmetric function f(x, y) where associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randic index follow as corollaries. The extremal structures...
General numeration II. Division schemes.
This is the second in a series of two papers on numeration schemes. Whereas the first paper emphasized grouping as exemplified in the partition of a number so as to obtain its base two numeral, the present paper takes at its point of departure the method of repeated divisions, as in the calculation of the base two numeral for a number by dividing it by two, then dividing the quotient by two, etc., and collecting the remainders. This method is a sort of classification scheme - odd or even.