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The Maximum Spectral Radius of Graphs without Spanning Linear Forests

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (1)

Given a family F of graphs, a graph G is called F-free if G contains none of F as its subgraph. The following problem is one of the most concerned pro......

An Exponential Bound for Simultaneous Embeddings of Planar Graphs

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (5)

We show that there are O(n . 4(n/11)) planar graphs on n vertices which do not admit a simultaneous straight-line embedding on any n-point set in the ......

On 4-Sachs Optimal Graphs

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (4)

Let G be a graph with order n and adjacency matrix A(G). The adjacency polynomial of G is defined as phi(G;lambda) = det(lambda I - A(G)) = Sigma(n)(i......

Intersection Graphs of Maximal Sub-polygons of k-Lizards

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (4)

We introduce k-maximal sub-polygon graphs (k-MSP graphs), the intersection graphs of maximal polygons contained in a polygon with sides parallel to a ......

Size Gallai-Ramsey Number

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (6)

The size Ramsey number (r) over cap (G, H) of two graphs G, H, introduced by Erdos et al., is defined as (r) over cap (G, H) = min{|E(F)| : F -> (G......

New Results on k-independence of Hypergraphs

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (1)

Let H = (V, E) be an s-uniform hypergraph of order n and k >= 0 be an integer. A k-independent set S subset of V is a set of vertices such that the......

Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (2)

An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidi......

Generalized Delannoy Matrices and Their Combinatorial Properties

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (2)

In this paper, we concentrate on the generalized Delannoy paths with steps N-j = (0, j) for j >= 1, D-i = (1, i) for i >= 0 and D '(h) = (2, h) ......

Coloring Squares of Planar Graphs with Maximum Degree at Most Five

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (2)

The square G(2) of a graph G is the graph on the same vertex set as G in which two vertices u, v are adjacent if and only if uv is an element of E(G),......

Two Completely Independent Spanning Trees of P4-Free Graphs

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (2)

A graph without induced subgraphs isomorphic to a path of length 3 is P-4-free. If a graph G contains two spanning trees T-1, T-2 such that for each t......

2-Reconstructibility of Strongly Regular Graphs and 2-Partially Distance-Regular Graphs

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (5)

A graph is l-reconstructible if it is determined by its multiset of induced subgraphs obtained by deleting l vertices. For graphs with at least six ve......

On a Conjecture About Strong Pattern Avoidance

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (1)

In 2019, Bona and Smith introduced the definition of strong pattern avoidance, that is, a permutation pi strongly avoids a pattern sigma if pi and pi(......

Turan Problems for k-Geodetic Digraphs

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (2)

A digraph G is k -geodetic if for any pair of (not necessarily distinct) vertices u, v is an element of V (G) there is at most one walk of length <......

Spectral Radius and Fractional Perfect Matchings in Graphs

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (3)

For an n-vertex graph G, a fractional matching of G is a function f giving each edge a real number in [0, 1] such that Sigma(e is an element of Gamma ......

Upper Bounds on the Chromatic Polynomial of a Connected Graph with Fixed Clique Number

期刊: GRAPHS AND COMBINATORICS, 2023; 39 (3)

Let Ft (n) denote the family of all connected graphs of ordern with clique number t. In this paper, we present a new upper bound for the chromatic pol......

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