Dress A, Grünewald S. Semiharmonic trees and monocyclic graphs. Applied Mathematics Letters. 2003;16(8):1329-1332.A graph G is defined to be semiharmonic if there is a constant mu (necessarily a natural number) such that, for every vertex v, the number of walks of length 3 starting in v equals mud(G)(v) where d(G)(v) is the degree of v. We determine all finite semiharmonic trees and monocyclic graphs. (C) 2003 Elsevier Ltd. All rights reserved
We shall study degree-monotone paths in graphs, a problem inspired by the celebrated theorem of Erdo...
A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is iso...
By a graph G = (V,E) we mean a finite undirected connected graph without loops or multiple edges. Th...
AbstractA graph G is defined to be semiharmonic if there is a constant μ (necessarily a natural numb...
AbstractClassification of harmonic and semiharmonic graphs according to their cyclomatic number beca...
AbstractLet the trunk of a graph G be the graph obtained by removing all leaves of G. We prove that,...
For a connected graph , let be amonophonic diametral path of . A set is called a monophonic set of...
AbstractLet G be a graph on n vertices v1,v2,…,vn and let d(vi) be the degree (= number of first nei...
Abstract — For a connected graph G of order n, a subset S of vertices of G is a monophonic set of G ...
For any two vertices x and y in a connected graph G, an x–y path is a monophonic path if it contains...
AbstractFor any two vertices x and y in a connected graph G, an x–y path is a monophonic path if it ...
Abstract. For a connected graph G = (V, E) of order at least two, a set S of vertices of G is a mono...
22 pages, 6 figuresWe investigate Cayley graphs of finite semigroups and monoids. First, we look at ...
A set S of vertices of a connected graph G is a monophonic set if every vertex of G lies on an x−y m...
For a connected graph G of order n, a subset S of vertices of G is a monophonic set of G if each ver...
We shall study degree-monotone paths in graphs, a problem inspired by the celebrated theorem of Erdo...
A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is iso...
By a graph G = (V,E) we mean a finite undirected connected graph without loops or multiple edges. Th...
AbstractA graph G is defined to be semiharmonic if there is a constant μ (necessarily a natural numb...
AbstractClassification of harmonic and semiharmonic graphs according to their cyclomatic number beca...
AbstractLet the trunk of a graph G be the graph obtained by removing all leaves of G. We prove that,...
For a connected graph , let be amonophonic diametral path of . A set is called a monophonic set of...
AbstractLet G be a graph on n vertices v1,v2,…,vn and let d(vi) be the degree (= number of first nei...
Abstract — For a connected graph G of order n, a subset S of vertices of G is a monophonic set of G ...
For any two vertices x and y in a connected graph G, an x–y path is a monophonic path if it contains...
AbstractFor any two vertices x and y in a connected graph G, an x–y path is a monophonic path if it ...
Abstract. For a connected graph G = (V, E) of order at least two, a set S of vertices of G is a mono...
22 pages, 6 figuresWe investigate Cayley graphs of finite semigroups and monoids. First, we look at ...
A set S of vertices of a connected graph G is a monophonic set if every vertex of G lies on an x−y m...
For a connected graph G of order n, a subset S of vertices of G is a monophonic set of G if each ver...
We shall study degree-monotone paths in graphs, a problem inspired by the celebrated theorem of Erdo...
A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is iso...
By a graph G = (V,E) we mean a finite undirected connected graph without loops or multiple edges. Th...
DOI
Add to ORKG