Many applications involve measuring object similarity. When the objects are modeled by graphs, measuring the similarity turn into a graph matching problem, i.e., into the search for a best matching between the graphs vertices. In this paper, we address the problem of computing a graph similarity measure based on a multivalent graph matching. This measure has been shown generic in the sense that...

Description Given an undirected graph G = ( V, E ), a clique S is a subset of V such that for any two elements u, v ∈ S, ( u, v ) ∈ E. Using the notation ES to represent the subset of edges which have both endpoints in clique S, the induced graph GS = ( S, ES ) is complete. Finding the largest clique in a graph is an NP-hard problem, called the maximum clique problem (MCP). Cliques are intimate...

Graph similarity learning is a significant and fundamental issue in the theory analysis of graphs, which has been applied variety fields, including object tracking, recommender systems, search, etc. Recent methods for graph that utilize deep typically share two deficiencies: (1) they leverage neural networks as backbones representations but have not well captured complex information inside data...

In this paper, we address the retrieval of multi-modality medical volumes, which consist of two different imaging modalities, acquired sequentially, from the same scanner. One such example, positron emission tomography and computed tomography (PET-CT), provides physicians with complementary functional and anatomical features as well as spatial relationships and has led to improved cancer diagno...

Abstract The ability of molecular property prediction is great significance to drug discovery, human health, and environmental protection. Despite considerable efforts, quantitative various properties remains a challenge. Although some machine learning models, such as bidirectional encoder from transformer, can incorporate massive unlabeled data into representations via self-supervised strategy...

It has recently been observed by Zuiddam that finite graphs form a preordered commutative semiring under the graph homomorphism preorder together with join and disjunctive product as addition multiplication, respectively. This led to new characterization of Shannon capacity $\Theta$ via Strassen's Positivstellensatz: $\Theta(\bar{G}) = \inf_f f(G)$, where $f : \mathsf{Graph} \to \mathbb{R}_+$ r...

‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

The set of acyclic orientations of a connected graph with a given sink has a natural poset structure. We give a geometric proof of a result of Jim Propp: this poset is the disjoint union of distributive lattices. Let G be a connected graph on the vertex set [n] = {0} ∪ [n], where [n] denotes the set {1, . . . , n}. Let P denote the collection of acyclic orientations of G, and let P0 denote the ...

The study of self-duality has attracted some attention over the past decade. A good deal of research in that time has been done on constructing and classifying all self-dual graphs and in particular polyhedra. We will give an overview of the recent research in the first two chapters. In the third chapter, we will show the necessary condition that a self-complementary self-dual graph have n ≡ 0,...