Related papers: Comparing Graphs of Different Sizes
Each graph and choice of a commutative ring gives rise to an associated graphical group. In this article, we introduce and investigate graph polynomials that enumerate conjugacy classes of graphical groups over finite fields according to…
Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing…
For a graph $G$, let $\lambda_1(G)$ and $\lambda_2(G)$ denote the largest and the second largest adjacency eigenvalue of $G$. The sum $\lambda_1(G) + \lambda_2(G)$ is called the \emph{spectral sum} of $G$. We investigate the spectral sum of…
We find the asymptotic number of connected graphs with $k$ vertices and $k-1+l$ edges when $k,l$ approach infinity, reproving a result of Bender, Canfield and McKay. We use the {\em probabilistic method}, analyzing breadth-first search on…
We present the theory of multifunctions applied to graphs. Its interesting feature is that walks are recognized as iterations. We consider the graphs with arbitrary number of vertices which are determined by multifunctions. The mutually…
In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
We prove that the existence of a non-special tree of size $\lambda$ is equivalent to the existence of an uncountably chromatic graph with no $K_{\omega_1}$ minor of size $\lambda$, establishing a connection between the special tree number…
Whereas for strings, higher-order empirical entropy is the standard entropy measure, several different notions of empirical entropy for trees have been proposed in the past, notably label entropy, degree entropy, conditional versions of the…
Graph comparison is fundamentally important for many applications such as the analysis of social networks and biological data and has been a significant research area in the pattern recognition and pattern analysis domains. Nowadays, the…
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…
The problem of spanning trees is closely related to various interesting problems in the area of statistical physics, but determining the number of spanning trees in general networks is computationally intractable. In this paper, we perform…
Building on work by Desjarlais, Molina, Faase, and others, a general method is obtained for counting the number of spanning trees of graphs that are a product of an arbitrary graph and either a path or a cycle, of which grid graphs are a…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
A graph $G$ is defined encapsulating the number theoretic notion of the Fundamental Theorem of Arithmetic. We then provide a graph theoretic approach to the fundamental results on the coprimality of two natural numbers, through the use of…
We study various classes of random processes defined on the regular tree $T_d$ that are invariant under the automorphism group of $T_d$. Most important ones are factor of i.i.d. processes (randomized local algorithms), branching Markov…
We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs,…
The scramble number of a graph provides a lower bound for gonality and an upper bound for treewidth, making it a graph invariant of interest. In this paper we study graphs of scramble number at most two, and give a classification of all…
In this paper, we consider various graphs, namely: power graph, cyclic graph, enhanced power graph and commuting graph, on a finite semigroup $S$. For an arbitrary pair of these four graphs, we classify finite semigroups such that the…
Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest…
We describe a robust methodology, based on the martingale argument of Nachmias and Peres and random walk estimates, to obtain simple upper and lower bounds on the size of a maximal component in several random graphs \textit{at criticality}.…