Characterizing regular covers of symmetric graphs is one the fundamental topics in field algebraic graph theory, and often a key step for approaching general graphs. Complete graphs, which are typical naturally appear study many as normal quotient In this paper, characterization edge-transitive cyclic complete with prime power order given by using techniques finite group theory related properti...

9 Let X be a tree and letG=Aut(X), Bass and Tits have given an algorithm to construct the ‘ultimate quotient’ of X by G starting with any quotient of X, an ‘edge-indexed’ graph. Using a sequence of 11 integers that we compute at consecutive steps of the Bass–Tits (BT) algorithm, we give a lower bound on the diameter of the ultimate quotient of a tree by its automorphism group. For a tree X with...

We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for splice-quotient singularities with smaller resolution graphs. We also discuss the dimension of the first cohomology groups of certain invertible sheaves on a res...

We apply the quotient graph theory described by Band, Berkolaiko, Joyner and Liu to particular graphs symmetric with respect $S_3$ $C_3$ symmetry groups. find for three-edge star quantum Neumann boundary conditions at loose ends three types of coupling central vertex (standard, $\delta$ preferred-orientation coupling). These are smaller than original direct sum Hamiltonians is unitarily equival...

What is the shape of space in a spacetime? One way of addressing this issue is to consider edgeless spacelike submanifolds of the spacetime. An alternative is to foliate the spacetime by timelike curves and consider the quotient obtained by identifying points on the same timelike curve. In this article we investigate each of these notions and obtain conditions such that it yields a meaningful s...

— Concerning algebraic grammars in reduced form, bisimulation in the graph ofleft dérivations is known to be décidable. The quotient of the above graph by ils greatest bisimulation, called the canonical graph, is indeed isomorphic to the graph ofleft dérivations for another algebraic grammar in reduced form, produced by an effective procedure.

‎A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$‎, ‎denoted by match$(G)$‎. ‎In this paper‎, ‎we provide a generalization of this result for powers of edge ideals‎. ‎More precisely‎, ‎we show that for every graph $G$ and every $sgeq 1$‎, ‎$${rm reg}( R‎/ ‎I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...

Edge-colorings are used to extend the notion of the graph Cartesian product to a quotient operation that allows for the formation of graph fractions. Fractional graphs form a group that is isomorphic to the positive rational numbers.

This paper forms part of a study of 2-arc transitivity for finite imprimitive symmetric graphs, namely for graphs admitting an automorphism groupG that is transitive on ordered pairs of adjacent vertices, and leaves invariant a nontrivial vertex partition B. Such a group G is also transitive on the ordered pairs of adjacent vertices of the quotient graph B corresponding toB. If in additionG is ...