Discrete Applied Mathematics

In this paper, we primarily focus on the eigenvalues of the adjacency matrix and Seidel matrix of chain graphs, referred to as eigenvalues and Seidel eigenvalues of these graphs, respectively. Firstly, we utilize the characteristic polynomial of ...

For integer k ≥ 2, a graph G is called k-leaf-connected if | V ( G ) | ≥ k + 1 and given any subset S ⊆ V ( G ) with | S | = k, G always has a spanning tree T such that S is precisely the set of leaves of T. Thus a graph is 2-leaf-connected if ...

• A sharp bound on the first Zagreb index that ensures k-leaf-connected is given.
• A sharp bound on reciprocal degree distance that ensures k-leaf-connected is given.
• A sharp bound on the forgotten topological index that ensures k-...

Four Color Theorem implies that the independence number of every planar graph is at least n / 4. A cactus graph is a connected planar graph whose block is either an edge or a cycle. In this paper, the lower bound for independence number of cactus ...

Cyclic vertex connectivity c κ and cyclic edge connectivity c λ are two important kinds of conditional connectivity, which reflect the number of vertices or edges that can be removed before the graph is disconnected and at least two components ...

A total dominating set in a graph G is a set S of vertices of G such that every vertex in G is adjacent to a vertex in S. Recently, the following question was proposed:

“Is it true that every connected cubic graph containing a 3-cycle has two ...

The classical Shapley value for cooperative games determines a payoff vector considering that the formation of the grand coalition is made by incorporating players one by one. Later, this method was generalized for games with restricted ...

The domination game is played on a graph G by two players, Dominator and Staller, who alternate in selecting vertices until each vertex in the graph G is contained in the closed neighbourhood of the set of selected vertices. Dominator’s aim is to ...

A lossless data compression code based on a binary-coded ternary number representation is investigated. The code is complete, universal, synchronizable, and supports a direct search in a compressed file. A simple monotonous encoding and very fast ...

A connected graph G is H-removable if H is a subgraph of G, G has at least | V ( H ) | + 2 vertices and G − V ( H ′ ) has a perfect matching for every subgraph H ′ of G isomorphic to H. So a connected graph is k K 2-removable if and only if it is ...

For a vertex v of a graph, the local complementation at v is an operation that replaces the neighborhood of v by its complement graph. Two graphs are locally equivalent if one is obtained from the other by a sequence of local complementations. A ...