PATHOS DEGREE PRIME GRAPH OF A TREE

Let T be a tree of order n (n [greater than or equal to] 2). A pathos degree prime graph of T, written PDP (T), is a graph whose vertices are the vertices and paths of a pathos of T, with two vertices of PDP(T) adjacent whenever the degree of the corresponding vertices of T are unequal and relativel...

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Published inTWMS journal of applied and engineering mathematics Vol. 13; no. 1; p. 53
Main Author Nagesh, H. M
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2023
Elman Hasanoglu
Subjects
Apexes
Graph theory
Graphs
Mathematical research
India
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ISSN2146-1147
2146-1147

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Abstract Let T be a tree of order n (n [greater than or equal to] 2). A pathos degree prime graph of T, written PDP (T), is a graph whose vertices are the vertices and paths of a pathos of T, with two vertices of PDP(T) adjacent whenever the degree of the corresponding vertices of T are unequal and relatively prime; or the corresponding paths [P'.sub.i] and [P'.sub.j] (i [not equal to] j) of a pathos of T have a vertex in common; or one corresponds to the path P and the other to a vertex v and P begins (or ends) at v such that v is a pendant vertex in T. We look at some properties of this graph operator. For this class of graphs we discuss the planarity; outerplanarity; maximal outerplanarity; minimally nonouterplanarity; Eulerian; and Hamiltonian properties these graphs. Keywords: Crossing number, inner vertex number, pathos, path number. AMS Subject Classification: 05C05, 05C45.
AbstractList Let T be a tree of order n (n 2). A pathos degree prime graph of T, written PDP(T), is a graph whose vertices are the vertices and paths of a pathos of T, with two vertices of PDP(T) adjacent whenever the degree of the corresponding vertices of T are unequal and relatively prime; or the corresponding paths P 0 i and P 0 j (i 6= j) of a pathos of T have a vertex in common; or one corresponds to the path P 0 and the other to a vertex v and P 0 begins (or ends) at v such that v is a pendant vertex in T. We look at some properties of this graph operator. For this class of graphs we discuss the pla- narity; outerplanarity; maximal outerplanarity; minimally nonouterplanarity; Eulerian; and Hamiltonian properties these graphs.
Let T be a tree of order n (n [greater than or equal to] 2). A pathos degree prime graph of T, written PDP (T), is a graph whose vertices are the vertices and paths of a pathos of T, with two vertices of PDP(T) adjacent whenever the degree of the corresponding vertices of T are unequal and relatively prime; or the corresponding paths [P'.sub.i] and [P'.sub.j] (i [not equal to] j) of a pathos of T have a vertex in common; or one corresponds to the path P and the other to a vertex v and P begins (or ends) at v such that v is a pendant vertex in T. We look at some properties of this graph operator. For this class of graphs we discuss the planarity; outerplanarity; maximal outerplanarity; minimally nonouterplanarity; Eulerian; and Hamiltonian properties these graphs. Keywords: Crossing number, inner vertex number, pathos, path number. AMS Subject Classification: 05C05, 05C45.
Let T be a tree of order n (n [greater than or equal to] 2). A pathos degree prime graph of T, written PDP (T), is a graph whose vertices are the vertices and paths of a pathos of T, with two vertices of PDP(T) adjacent whenever the degree of the corresponding vertices of T are unequal and relatively prime; or the corresponding paths [P'.sub.i] and [P'.sub.j] (i [not equal to] j) of a pathos of T have a vertex in common; or one corresponds to the path P and the other to a vertex v and P begins (or ends) at v such that v is a pendant vertex in T. We look at some properties of this graph operator. For this class of graphs we discuss the planarity; outerplanarity; maximal outerplanarity; minimally nonouterplanarity; Eulerian; and Hamiltonian properties these graphs.
Audience Academic
Author Nagesh, H. M
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Elman Hasanoglu
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Snippet Let T be a tree of order n (n [greater than or equal to] 2). A pathos degree prime graph of T, written PDP (T), is a graph whose vertices are the vertices and...
Let T be a tree of order n (n 2). A pathos degree prime graph of T, written PDP(T), is a graph whose vertices are the vertices and paths of a pathos of T, with...
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SubjectTerms Apexes
Graph theory
Graphs
Mathematical research
Title PATHOS DEGREE PRIME GRAPH OF A TREE
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