A Cayley graph Cay(G,S) on a group G with respect to a Cayley subset S is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of Cay(G,S). For a positive integer n, let Γn be a graph having vertex set {xi, yi | i ∈ Z2n} and edge set {{xi, xi+1}, {yi, yi+1}, {x2i, y2i+1}, {y2i, x2i+1} | i ∈ Z2n}. In this paper, it is shown that Γn is a Cayley ...

Infinite normal forms are a way of giving semantics to non-terminating rewrite systems. The notion is a generalization of the Böhm tree in the lambda calculus. It was first introduced in [AB97] to provide semantics for a lambda calculus on terms with letrec. In that paper infinite normal forms were defined directly on the graph rewrite system. In [Blo01] the framework was improved by defining t...

altan derivatives of polycyclic conjugated hydrocarbons were recently introduced and studied in theoretical organic chemistry. we now provide a generalization of the altan concept, applicable to any graph. several earlier noticed topological properties of altan derivatives of polycyclic conjugated hydrocarbons are shown to be the properties of all altan derivatives of all graphs. among these ar...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

All planar graphs are 4-colorable and 5-choosable, while some planar graphs are not 4-choosable. Determining which properties guarantee that a planar graph can be colored using lists of size four has received significant attention. In terms of constraining the structure of the graph, for any l∈{3,4,5,6,7}" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; ...

We present two short proofs for Diestel's criterion that a connected graph has normal spanning tree provided it contains no subdivision of countable clique in which every edge been replaced by uncountably many parallel edges.

In this paper, we determine all of connected normal edge-transitive Cayley graphs on non-abelian groups with order $4p^2$, where $p$ is a prime number.

The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomial-time algorithm...

a emph{signed graph} (or, in short, emph{sigraph}) $s=(s^u,sigma)$ consists of an underlying graph $s^u :=g=(v,e)$ and a function $sigma:e(s^u)longrightarrow {+,-}$, called the signature of $s$. a emph{marking} of $s$ is a function $mu:v(s)longrightarrow {+,-}$. the emph{canonical marking} of a signed graph $s$, denoted $mu_sigma$, is given as $$mu_sigma(v) := prod_{vwin e(s)}sigma(vw).$$the li...