On the structure and classification of SOMAs: Generalizations of mutually orthogonal Latin squares.
We study the structure of path-like trees. In order to do this, we introduce a set of trees that we call expandable trees. In this paper we also generalize the concept of path-like trees and we call such generalization generalized path-like trees. As in the case of path-like trees, generalized path-like trees, have very nice labeling properties.
A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is known that a plane graph of minimum face size 5 contains light paths and a light pentagon. In this paper we show that every plane graph of minimum face size 5 contains also a light star and we present a structural result concerning the existence of a pair of adjacent faces with degree-bounded vertices.
We show that for any relatively prime integers 1 ≤ p < q and for any finite A ⊂ ℤ one has .
For a bipartite graph and a non-zero real , we give bounds for the sum of the th powers of the Laplacian eigenvalues of using the sum of the squares of degrees, from which lower and upper bounds for the incidence energy, and lower bounds for the Kirchhoff index and the Laplacian Estrada index are deduced.