• Journal of applied mathematics & informatics
• /
• 제31권5_6호
• /
• pp.595-608
• /
• 2013

Let G = (V, E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V (G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The distance between the vertices $u$ and $v$ in V (G) of graph G is the number of edges in a shortest path connecting them, we denote by $d(u,v)$. In graph theory, we have many invariant polynomials for a graph G. In this paper, we focus on the Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and their topological indices of a molecular graph circumcoronene series of benzenoid $H_k$ and specially third member from this family. $H_3$ is a basic member from the circumcoronene series of benzenoid and its conclusions are base calculations for the Schultz polynomial and Hosoya polynomial of the circumcoronene series of benzenoid $H_k$ ($k{\geq}3$).

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제17권11호
• /
• pp.2903-2923
• /
• 2023

Knowledge recommendation is a type of recommendation system that recommends knowledge content to users in order to satisfy their needs. Although using graph neural networks to extract data features is an effective method for solving the recommendation problem, there is information loss when modeling real-world problems because an edge in a graph structure can only be associated with two nodes. Because one super-edge in the hypergraph structure can be connected with several nodes and the effectiveness of knowledge graph for knowledge expression, a dual-channel hypergraph convolutional neural network model (DCHC) based on hypergraph structure and knowledge graph is proposed. The model divides user data and knowledge data into user subhypergraph and knowledge subhypergraph, respectively, and extracts user data features by dual-channel hypergraph convolution and knowledge data features by combining with knowledge graph technology, and finally generates recommendation results based on the obtained user embedding and knowledge embedding. The performance of DCHC model is higher than the comparative model under AUC and F1 evaluation indicators, comparative experiments with the baseline also demonstrate the validity of DCHC model.

• Journal of applied mathematics & informatics
• /
• 제34권3_4호
• /
• pp.341-354
• /
• 2016

In this paper, the exact formulae for the generalized product degree distance, reciprocal product degree distance and product degree distance of tensor product of a connected graph and the complete multipartite graph with partite sets of sizes m₀, m₁, ⋯ , m_r−1 are obtained.

• Journal of applied mathematics & informatics
• /
• 제4권1호
• /
• pp.235-242
• /
• 1997

We characterize the tight structure of a vertex-accumula-tion-free maximal planar graph with no separating triangles. Together with the result of Halin who gave an equivalent form for such graphs this yields that a tight structure always exists in every 4-connected maximal planar graph with one end.

• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.851-860
• /
• 2008

A countable locally finite triangulation is a strong triangulation if a representation of the graph contains no vertex- or edge-accumulation points. In this paper we exhibit the structure of an infinite strong triangulation and prove the existence of connected spanning subgraph with maximum degree 4 in such a graph

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.531-539
• /
• 2009

In this paper we first present a structure theorem for an infinite locally finite 3-connected VAP-free planar graph, and in connection with this result we study a possible classification of infinite locally finite planar graphs by reducing modulo finiteness.

• Journal of applied mathematics & informatics
• /
• 제28권3_4호
• /
• pp.909-912
• /
• 2010

In this note we present a short proof of the following result by Zhou, Liu and Xu. Let G be a graph of order n, and let a and b be two integers with 1 $\leq$ a < b and b $\geq$ 3, and let g and f be two integer-valued functions defined on V(G) such that a $\leq$ g(x) < f(x) $\leq$ b for each $x\;{\in}\;V(G)$ and f(V(G)) - V(G) even. If $n\;{\geq}\;\frac{(a+b-1)^2+1}{a}$ and $\delta(G)\;{\geq}\;\frac{(b-1)n}{a+b-1}$,then G has a connected (g, f)-factor.

• Journal of applied mathematics & informatics
• /
• 제24권1_2호
• /
• pp.141-154
• /
• 2007

The connectivity problem is a fundamental problem in graph theory. The best known algorithm to solve the connectivity problem on general graphs with n vertices and m edges takes $O(K(G)mn^{1.5})$ time, where K(G) is the vertex connectivity of G. In this paper, an efficient algorithm is designed to solve vertex connectivity problem, which takes $O(n^2)$ time and O(n) space for a trapezoid graph.

• 한국통신학회논문지
• /
• 제13권1호
• /
• pp.63-73
• /
• 1988

본 논문에서는 확률적 방향성 그래프에서 시점(source node)과 종점(terminal node) 간의 통신할 수 있는 확률인 단점간 신뢰도를 계정하는 알고리즘을 제시하였다. Satyanarayana의 factoring $theorem^{(7)}$을 이용하여 확률적 방향성 그래프에서 시점에 연결되어 있는 에지(edge)를 개방(open)과 단락(short)상태로 감축하여 원래의 그래프를 2개의 감축된 그래프로 분리한 후, 본 논문이 제시한 에지제거법과 일반적인 직, 병렬 감축법을 분리된 그래프에 적용한다. 이 에지 감축(edge reduction)을 source node와 terminal node가 단일 에지로 연결될때까지 반복한다. 또한 복잡하고 규모가 큰 망에 대한 단점간 신뢰도를 계정하기 위해서 전산기 프로그램을 제시하였다.

• 대한수학회지
• /
• 제60권5호
• /
• pp.959-986
• /
• 2023

Zhai and Lin recently proved that if G is an n-vertex connected 𝜃(1, 2, r + 1)-free graph, then for odd r and n ⩾ 10r, or for even r and n ⩾ 7r, one has ${\rho}(G){\leq}{\sqrt{{\lfloor}{\frac{n^2}{4}}{\rfloor}}}$, and equality holds if and only if G is $K_{{\lceil}{\frac{n}{2}}{\rceil},{\lfloor}{\frac{n}{2}}{\rfloor}}$. In this paper, for large enough n, we prove a sharp upper bound for the spectral radius in an n-vertex H-free non-bipartite graph, where H is 𝜃(1, 2, 3) or 𝜃(1, 2, 4), and we characterize all the extremal graphs. Furthermore, for n ⩾ 137, we determine the maximum number of edges in an n-vertex 𝜃(1, 2, 4)-free non-bipartite graph and characterize the unique extremal graph.