Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investigation of the relation between properties of a graph and the spectrum of its adjacency matrix. A ce...

This paper presents a general, non-procedural, algebraic approach to graphical analysis of structures. Using graph theoretical properties of reciprocal graphs, the geometrical relation between the form and force diagrams used in graphic statics is written algebraically. These formulations have been found to be equivalent to the equilibrium equations used in matrix analysis of planar, self-stres...

Simeon Ball, Universitat Politécnica de Catalunya On subsets of a finite vector space in which every subset of basis size is a basis In this talk we consider sets of vectors S of the vector space Fq with the property that every subset of S of size k is a basis. The classical example of such a set is the following. Example (Normal Rational Curve) The set S = {(1, t, t, . . . , tk−1) | t ∈ Fq} ∪ ...

The intersection graph $mathbb{Int}(A)$ of an $S$-act $A$ over a semigroup $S$ is an undirected simple graph whose vertices are non-trivial subacts of $A$, and two distinct vertices are adjacent if and only if they have a non-empty intersection. In this paper, we study some graph-theoretic properties of $mathbb{Int}(A)$ in connection to some algebraic properties of $A$. It is proved that the fi...