On Some Solved and Unsolved Problems of Chemical Graph Theory - Trinajstic, Klein, et al. - 1986Nenad Trinajstic, Douglas J. Klein, and Milan Randic. On some solved and unsolved prob- lems of chemical graph theory. International Journal of Quantum Chemistry, 30(S20):699- 742, 1986....
NP-Complete Problems in Graph Theory - Explore NP-Complete problems in Graph Theory, their significance, and implications in computational complexity.
2. Two long-standing problems in graph theory Two long-standing problems in graph theory are the skew partition problem and the clique graph problem. The skew partition problem was defined by Chvátal in 1985 as the recognition problem for a special decomposition arising in the context of perfect...
4.5 Graph theory Graph theory is a mathematical tool that is broadly used to model pairwise interactions among objects. In this, a highly computational complex problem could be solved by designing and analyzing the graph model. Therefore, the graph theory is widely used in different scenarios of...
inverse problems were solved forΓ3by Makhnev and Nirova. In this paper, we study the intersection arrays of distance-regular graphΓof diameter 3, for which the graphΓ¯3is a pseudo-geometric graph of the netPGm(n,m). New infinite series of admissible intersection arrays for these gr...
(under standard assumptions from complexity theory) is the wreath product \(s_5 \wr \mathbb {z}\) (where \(s_5\) is the symmetric group on 5 elements). the word problem for this group can be easily solved in logspace, whereas the power word problem for \(s_5 \wr \mathbb {z}\...
Models are extremely important in modern network theory. It can be argued that the discovery of models for very large networks with a mixture of randomness and order lies at the heart of the transition from conventional graph theory to the modern science of networks. Here we describe three prot...
Graph theory has been almost 300 years since its birth, but have not been well solved many problems. With the development of computer science, graph theory again become a place where people discuss hot spots, here are some applications of graph theory in real life. ...
1163Accesses Abstract The most common application of graph theory is search problems. Using graph theory, this project aims to solve one such NP-hard problem, i.e., finding a path for a Rubik’s cube to reach the solved state from a scrambled one. Rubik’s cube is among one of the fa...
Graph Theory Optimization Problem Solving Use our pre-submission checklist Avoid common mistakes on your manuscript. 1 Introduction Frei et al. [1] comprehensively studied the problem of how stable certain central graph parameters are when a given graph is slightly modified, i.e., under oper...